Tron Omland

• Haugland, Jan Kristian & Omland, Tron (2025). Shift-invariant transformations and almost liftings. Cryptography and Communications. ISSN 1936-2447. doi: 10.1007/s12095-025-00848-w. Fulltekst i vitenarkiv Vis sammendrag

  We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on n bits that are induced from Boolean functions on k bits, for k ≤ n. We consider such transformations that are not necessarily permutations, but are, in some sense, almost bijective, and study their cryptographic properties. In this context, we define an almost lifting as a Boolean function for which there is an upper bound on the number of collisions of its induced transformation that does not depend on n. We show that if a Boolean function with diameter k is an almost lifting, then the maximum number of collisions of its induced transformation is 2k−1 for any n. Moreover, we search for functions in the class of almost liftings that have good cryptographic properties and for which the non-bijectivity does not cause major security weaknesses. These functions generalize the well-known map χ used in the Keccak hash function

• Aguilar, Konrad; Behera, Karina; Omland, Tron & Wu, Nicole (2025). On the Bures metric, C*-norm and quantum metric. Bulletin of the Australian Mathematical Society. ISSN 0004-9727. 112(2), s. 355–365. doi: 10.1017/S0004972724001217. Fulltekst i vitenarkiv
• Bedos, Eric Christophe & Omland, Tron (2023). C*-irreducibility for reduced twisted group C*-algebras. Journal of Functional Analysis. ISSN 0022-1236. 284(5), s. 109795–109826. doi: 10.1016/j.jfa.2022.109795. Fulltekst i vitenarkiv Vis sammendrag

  We study C*-irreducibility of inclusions of reduced twisted group C*-algebras and of reduced group C*-algebras. We characterize C*-irreducibility in the case of an inclusion arising from a normal subgroup, and exhibit many new examples of C*-irreducible inclusions.

• Kaliszewski, S.; Omland, Tron; Quigg, Johnnie Currie & Turk, Jonathan (2023). Strong Pedersen rigidity for coactions of compact groups. International Journal of Mathematics. ISSN 0129-167X. 34(13). doi: 10.1142/S0129167X23500830. Fulltekst i vitenarkiv Vis sammendrag

  We prove a version of Pedersen’s outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of the dual actions. In fact, we show that every isomorphism of a dual action comes from a unique outer conjugacy of a coaction, which in this context should be called strong Pedersen rigidity. We promote this to a category equivalence.

• Enstad, Ulrik Bo Rufus; Jakobsen, Mads Sielemann; Luef, Franz & Omland, Tron (2022). Deformations and Balian-Low theorems for Gabor frames on the adeles. Advances in Mathematics. ISSN 0001-8708. 410. doi: 10.1016/j.aim.2022.108771. Fulltekst i vitenarkiv
• Li, Xin; Omland, Tron & Spielberg, Jack (2020). C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics. ISSN 0010-3616. 381(3), s. 1263–1308. doi: 10.1007/s00220-020-03758-5. Fulltekst i vitenarkiv Vis sammendrag

  WestudyC*-algebrasgeneratedbyleftregularrepresentationsofrightLCM one-relator monoids and Artin–Tits monoids of finite type. We obtain structural results concerning nuclearity, ideal structure and pure infiniteness. Moreover, we compute K- theory. Based on our K-theory results, we develop a new way of computing K-theory for certain group C*-algebras and crossed products.

• Bryder, Rasmus Sylvester; Ivanov, Nikolay A. & Omland, Tron (2020). C∗-simplicity of hnn extensions and groups acting on trees. Annales de l'Institut Fourier. ISSN 0373-0956. 70(4), s. 1497–1543. doi: 10.5802/AIF.3378. Fulltekst i vitenarkiv Vis sammendrag

  We study non-ascending HNN extensions acting on their Bass– Serre tree and characterize C∗-simplicity and the unique trace property by means of the kernel and quasi-kernels of the HNN extension in question. We also present a concrete example of an HNN extension that is a new example of a group that is not C∗-simple but does have the unique trace property. Additionally, we include certain more general results, mostly based on previous work of various authors, concerning C∗-simplicity of groups admitting extreme boundary actions, and in particular, groups acting on trees. Résumé. — Nous étudions les extensions HNN non-ascendantes agissant sur leur arbre de Bass–Serre and caractérisons la C∗-simplicité et la propriété d’unicité de la trace à l’aide du noyau et des quasi-noyaux des extensions HNN en question. Nous présentons aussi un exemple concret d’extension HNN fournissant un nouvel exemple de groupe C∗-simple mais ne possédant pas la propriété d’unicité de la trace. De plus, nous obtenons certains resultats plus généraux, la plupart se fondant sur des travaux antérieurs d’auteurs divers, concernant la C∗-simplicité de groupes admettant des actions extrêmes sur des bords, et, en particulier, de groupes agissant sur des arbres.

• Omland, Tron (2019). Dynamical systems and operator algebras associated to Artin's representation of braid groups. Journal of operator theory. ISSN 0379-4024. 83(1), s. 55–72. doi: 10.7900/jot.2018jun12.2217. Fulltekst i vitenarkiv
• Kaliszewski, S.; Omland, Tron & Quigg, John (2019). The Pedersen Rigidity problem. Revista Colombiana de Matematicas. ISSN 0034-7426. 53(E), s. 237–277. doi: 10.15446/RECOLMA.V53NSUPL.84095. Fulltekst i vitenarkiv
• Omland, Tron (2019). Free nilpotent groups are C*-superrigid. Proceedings of the American Mathematical Society. ISSN 0002-9939. 148(1), s. 283–287. doi: 10.1090/proc/14678. Fulltekst i vitenarkiv Vis sammendrag

  The free nilpotent group Gm,n of class m and rank n is the free object on n generators in the category of nilpotent groups of class at most m. We show that Gm,n can be recovered from its reduced group C∗-algebra, in the sense that if H is any group such that C∗ r(H) is isomorphic to C∗ r(Gm,n), then H must be isomorphic to Gm,n.

• Kaliszewski, S.; Omland, Tron & Quigg, John (2019). Rigidity theory for C*-dynamical systems and the "Pedersen rigidity problem", II. International Journal of Mathematics. ISSN 0129-167X. 30(8). doi: 10.1142/S0129167X19500381. Fulltekst i vitenarkiv Vis sammendrag

  This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen’s theorem, which does hold for an arbitrary locally compact group G G , saying that two actions (A,α) (A,α) and (B,β) (B,β) of G G are outer conjugate if and only if the dual coactions (A ⋊ α G, α ˆ ) (A⋊αG,α̂) and (B ⋊ β G, β ˆ ) (B⋊βG,β̂) of G G are conjugate via an isomorphism that maps the image of A A onto the image of B B (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images; and we have decided to use the term “Pedersen rigid” for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call “fixed-point rigidity”. In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.

• Kaliszewski, S.; Omland, Tron & Quigg, John (2018). Rigidity theory for C*-dynamical systems and the "Pedersen rigidity problem". International Journal of Mathematics. ISSN 0129-167X. 29(3). doi: 10.1142/S0129167X18500167. Fulltekst i vitenarkiv
• Bédos, Erik & Omland, Tron (2018). On reduced twisted group C*-algebras that are simple and/or have a unique trace. Journal of Noncommutative Geometry. ISSN 1661-6952. 12(3), s. 947–996. doi: 10.4171/JNCG/295. Fulltekst i vitenarkiv Vis sammendrag

  On reduced twisted group C*-algebras that are simple and/or have a unique trace

• Omland, Tron (2017). How many Pythagorean triples with a given inradius? Journal of Number Theory. ISSN 0022-314X. 170, s. 1–2. doi: 10.1016/j.jnt.2016.06.009. Fulltekst i vitenarkiv
• Kaliszewski, S.; Omland, Tron & Quigg, John (2017). Dualities for maximal coactions. Journal of the Australian Mathematical Society. ISSN 1446-7887. 102(2), s. 224–254. doi: 10.1017/S1446788716000215. Fulltekst i vitenarkiv
• Kaliszewski, S.; Omland, Tron & Quigg, John (2016). Destabilization. Expositiones mathematicae. ISSN 0723-0869. 34(1), s. 62–81. doi: 10.1016/j.exmath.2015.10.003. Fulltekst i vitenarkiv
• Kaliszewski, S.; Omland, Tron & Quigg, John (2016). Three versions of categorical crossed-product duality. New York journal of mathematics. 22, s. 293–339. Fulltekst i vitenarkiv
• Ivanov, Nikolay A. & Omland, Tron (2016). C*-simplicity of free products with amalgamation and radical classes of groups. Journal of Functional Analysis. ISSN 0022-1236. 272(9), s. 3712–3741. doi: 10.1016/j.jfa.2016.12.011. Fulltekst i vitenarkiv
• Barlak, Selçuk; Omland, Tron & Stammeier, Nicolai (2016). On the K-theory of C*-algebras arising from integral dynamics. Ergodic Theory and Dynamical Systems. ISSN 0143-3857. 38(3), s. 832–862. doi: 10.1017/etds.2016.63. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the K -theory of unital UCT Kirchberg algebras QS arising from families S of relatively prime numbers. It is shown that K∗(QS) is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct C∗ -algebra naturally associated to S. The C∗ -algebra representing the torsion part is identified with a natural subalgebra AS of QS. For the K -theory of QS, the cardinality of S determines the free part and is also relevant for the torsion part, for which the greatest common divisor gS of {p−1:p∈S} plays a central role as well. In the case where |S|≤2 or gS=1 we obtain a complete classification for QS. Our results support the conjecture that AS coincides with ⊗p∈SOp. This would lead to a complete classification of QS, and is related to a conjecture about k -graphs. This research was first published in Ergodic Theory and Dynamical Research. © Cambridge University Press.

• Bédos, Erik & Omland, Tron (2016). On twisted group C∗-algebras associated with FC-hypercentral groups and other related groups. Ergodic Theory and Dynamical Systems. ISSN 0143-3857. 36(6), s. 1743–1756. doi: 10.1017/etds.2015.9. Fulltekst i vitenarkiv
• Omland, Tron Ånen (2015). C*-algebras generated by projective representations of free nilpotent groups. Journal of operator theory. ISSN 0379-4024. 73(1), s. 3–25. doi: 10.7900/jot.2013mar06.2037. Fulltekst i vitenarkiv
• Omland, Tron Ånen (2014). Primeness and primitivity conditions for twisted group C*-algebras. Mathematica Scandinavica. ISSN 0025-5521. 114(2), s. 299–319. doi: 10.7146/math.scand.a-17113. Fulltekst i vitenarkiv
• Kaliszewski, S.; Omland, Tron & Quigg, John (2014). Cuntz-Li algebras from a-adic numbers. Revue Roumaine de Mathématiques Pures et Appliquées. ISSN 0035-3965. 59(3), s. 331–370. Fulltekst i vitenarkiv
• Omland, Tron Ånen (2013). C∗-Algebras Associated with a-adic Numbers. I Carlsen, Toke Meier; Eilers, Søren; Silvestrov, Sergei & Restorff, Gunnar (Red.), Operator Algebra and Dynamics. Springer. ISSN 9783642394584. s. 223–238. doi: 10.1007/978-3-642-39459-1_11. Fulltekst i vitenarkiv
• Bedos, Erik Christopher & Omland, Tron Ånen (2012). The full group C*-algebra of the modular group is primitive. Proceedings of the American Mathematical Society. ISSN 0002-9939. 140(4), s. 1403–1411. Fulltekst i vitenarkiv
• Bedos, Erik Christopher & Omland, Tron Ånen (2011). Primitivity of some full group C*-algebras. Banach Journal of Mathematical Analysis. ISSN 2662-2033. 5(2), s. 44–58. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Omland, Tron (2025). Cryptography and national security in the quantum age. Fulltekst i vitenarkiv
• Omland, Tron (2025). Metrics on quantum channels from noncommutative geometry. Fulltekst i vitenarkiv
• Omland, Tron (2024). Shift-invariant functions and almost liftings. Fulltekst i vitenarkiv
• Omland, Tron (2024). Shift-invariant functions and almost liftings. Fulltekst i vitenarkiv
• Omland, Tron (2022). Open quantum walks. Fulltekst i vitenarkiv
• Omland, Tron (2022). Shift-invariant bijections. Fulltekst i vitenarkiv
• Omland, Tron (2021). C*-irreducibility for twisted group C*-algebras. Fulltekst i vitenarkiv
• Omland, Tron (2019). C*-algebras from rational dynamics. Fulltekst i vitenarkiv
• Omland, Tron (2019). Review of "C*-superrigidity of 2-step nilpotent groups" by Caleb Eckhardt and Sven Raum. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2018). Review of "Crossed products by Hecke pairs" by Rui Palma. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2018). Review of "An infinite C*-algebra with a dense, stably finite *-subalgebra." by Niels Jakob Laustsen and Jared T. White. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2018). C*-superrigidity for discrete groups. Fulltekst i vitenarkiv
• Omland, Tron (2018). Review of "On just-infiniteness of locally finite groups and their C*-algebras" by V. Belyaev, R. Grigorchuk, and P. Shumyatsky. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2018). Review of "C*-algebras associated to graphs of groups" by Nathan Brownlowe, Alexander Mundey, David Pask, Jack Spielberg, and Anne Thomas. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2017). Review of "Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras" by Ruy Exel and Enrique Pardo. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2017). C*-simplicity and radical classes of groups. Fulltekst i vitenarkiv
• Omland, Tron (2017). C*-algebras arising from integral and rational dynamics. Fulltekst i vitenarkiv
• Omland, Tron (2017). C*-simplicity and radical classes of groups. Fulltekst i vitenarkiv
• Omland, Tron (2017). C*-simplicity for groups acting on trees. Fulltekst i vitenarkiv
• Omland, Tron (2017). Rigidity theory for C*-dynamical systems and the "Pedersen Rigidity Problem". Fulltekst i vitenarkiv
• Omland, Tron (2016). Dynamical systems and operator algebras associated to Artin's representation of braid groups II. Fulltekst i vitenarkiv
• Omland, Tron (2016). Review of "Imprimitivity theorems for weakly proper actions of locally compact groups" by Alcides Buss and Siegfried Echterhoff. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2016). Dynamical systems and operator algebras associated to Artin's representation of braid groups I. Fulltekst i vitenarkiv
• Omland, Tron (2016). C*-simplicity of free products with amalgamation and radical classes of groups. Fulltekst i vitenarkiv
• Omland, Tron (2016). C*-simplicity of free products with amalgamation and radical classes of groups. Fulltekst i vitenarkiv
• Omland, Tron (2016). C*-algebras arising from integral dynamics. Fulltekst i vitenarkiv
• Omland, Tron (2015). Review of "On certain multiplier projections" by Henning Petzka. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2015). Review of "Property T and amenable transformation group C*-algebras" by F. Kamalov. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2015). On the K-theory of certain Cuntz-Li algebras. Fulltekst i vitenarkiv
• Omland, Tron (2015). Review of "Groupoid equivalence and the associated iterated crossed product" by Jonathan Henry Brown, Geoff Goehle, and Dana P. Williams. Mathematical Reviews. ISSN 0025-5629. Fulltekst i vitenarkiv
• Omland, Tron (2015). C*-algebras arising from integral dynamics. Fulltekst i vitenarkiv
• Omland, Tron (2014). Simple reduced twisted group C*-algebras with unique trace. Fulltekst i vitenarkiv
• Omland, Tron (2014). On simplicity and uniqueness of trace for reduced twisted group C*-algebras. Fulltekst i vitenarkiv
• Omland, Tron (2013). Cuntz-Li algebras from a-adic numbers. Fulltekst i vitenarkiv
• Omland, Tron Ånen (2013). On the structure of certain C*-algebras arising from groups. Norges teknisk-naturvitenskapelige universitet. ISSN 9788247144268. Fulltekst i vitenarkiv
• Bedos, Eric Christophe & Omland, Tron (2009). The full group C*-algebra of the modular group is primitive. Universitetet i Oslo. Fulltekst i vitenarkiv

Se alle arbeider i NVA