Sergiy Neshveyev

• Habbestad, Erik & Neshveyev, Sergey (2025). Subproduct systems with quantum group symmetry. II. Transactions of the American Mathematical Society. ISSN 0002-9947. 378, s. 5159–5185. doi: 10.1090/tran/9459. Fulltekst i vitenarkiv Vis sammendrag

  We complete our analysis of the Temperley–Lieb subproduct systems, which define quantum analogues of Arveson’s 2 -shift, by extending the main results of the previous paper to the general parameter case. Specifically, we show that the associated Toeplitz algebras are nuclear, find complete sets of relations for them, prove that they are equivariantly KK -equivalent to C and compute the K -theory of the associated Cuntz–Pimsner algebras. A key role is played by quantum symmetry groups, first studied by Mrozinski, preserving Temperley–Lieb polynomials up to rescaling, and their monoidal equivalence to Uq(2) . In Appendix we show how to adapt Voigt’s arguments for SUq(2) to establish the Baum–Connes conjecture for the dual of Uq(2) , which is needed in our analysis of K-theory.

• Laca, Marcelo; Neshveyev, Sergey & Yamashita, Makoto (2025). Crystallization of C∗-Algebras. Communications in Mathematical Physics. ISSN 0010-3616. 406(3). doi: 10.1007/s00220-024-05212-2. Fulltekst i vitenarkiv
• Christensen, Johannes & Neshveyev, Sergey (2024). Isotropy fibers of ideals in groupoid C*-algebras. Advances in Mathematics. ISSN 0001-8708. 447. doi: 10.1016/j.aim.2024.109696. Fulltekst i vitenarkiv Vis sammendrag

  Given a locally compact étale groupoid and an ideal I in its groupoid C⁎-algebra, we show that I defines a family of ideals in group C⁎-algebras of the isotropy groups and then study to which extent I is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; (c) classify the primitive ideals for a class of graded groupoids with essentially central isotropy.

• Habbestad, Erik & Neshveyev, Sergey (2024). Cocycle Twisting of Semidirect Products and Transmutation. International Mathematics Research Notices (IMRN). ISSN 1073-7928. 2024(11), s. 9142–9164. doi: 10.1093/imrn/rnae015. Fulltekst i vitenarkiv Vis sammendrag

  We apply Majid’s transmutation procedure to Hopf algebra maps H → C[T], where T is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of T by subgroups that are cocentral in H. This allows us to unify and generalize a number of recent constructions of braided compact quantum groups, starting from the braided SUq(2) quantum group, and describe their bosonizations.

• Habbestad, Erik & Neshveyev, Sergey (2024). Subproduct systems with quantum group symmetry. Journal of Noncommutative Geometry. ISSN 1661-6952. 18(1), s. 93–121. doi: 10.4171/JNCG/523. Fulltekst i vitenarkiv Vis sammendrag

  We introduce a class of subproduct systems of finite dimensional Hilbert spaces whose fibers are defined by the Jones–Wenzl projections in Temperley–Lieb algebras. The quantum symmetries of a subclass of these systems are the free orthogonal quantum groups. For this subclass, we show that the corresponding Toeplitz algebras are nuclear C*-algebras that are KK-equivalent to C and obtain a complete list of generators and relations for them. We also show that their gauge-invariant subalgebras coincide with the algebras of functions on the end compactifications of the duals of the free orthogonal quantum groups. Along the way we prove a few general results on equivariant subproduct systems, in particular, on the behavior of the Toeplitz and Cuntz–Pimsner algebras under monoidal equivalence of quantum symmetry groups.

• Bieliavsky, Pierre; Gayral, Victor; Neshveyev, Sergey & Tuset, Lars (2024). Quantization of locally compact groups associated with essentially bijective 1-cocycles. International Journal of Mathematics. ISSN 0129-167X. 35(08). doi: 10.1142/S0129167X24500277. Fulltekst i vitenarkiv Vis sammendrag

  Given an extension 0→V→G→Q→1 of locally compact groups, with V abelian, and a compatible essentially bijective 1-cocycle η:Q→ˆV, we define a dual unitary 2-cocycle on G and show that the associated deformation of Ĝ is a cocycle bicrossed product defined by a matched pair of subgroups of Q⋉ˆV. We also discuss an interpretation of our construction from the point of view of Kac cohomology for matched pairs. Our setup generalizes that of Etingof and Gelaki for finite groups and its extension due to Ben David and Ginosar, as well as our earlier work on locally compact groups satisfying the dual orbit condition. In particular, we get a locally compact quantum group from every involutive nondegenerate set-theoretical solution of the Yang–Baxter equation, or more generally, from every brace structure. On the technical side, the key new points are constructions of an irreducible projective representation of G on L2(Q) and a unitary quantization map L2(G)→HS(L2(Q)) of Kohn–Nirenberg type.

• Neshveyev, Sergey & Schwartz, Gaute (2023). Non-Hausdorff etale groupoids and C*-algebras of left cancellative monoids. Münster Journal of Mathematics. ISSN 1867-5778. 16(1), s. 147–175. doi: 10.17879/51009604279. Fulltekst i vitenarkiv
• Commer, Kenny De; Neshveyev, Sergiy; Tuset, Lars & Yamashita, Makoto (2023). Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik-Zamolodchikov equations and Letzter-Kolb coideals. Forum of Mathematics, Pi. 11. doi: 10.1017/fmp.2023.11. Fulltekst i vitenarkiv Vis sammendrag

  We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enriquez–Etingof cyclotomic Knizhnik– Zamolodchikov (KZ) equations and the other on the Letzter–Kolb coideals. This equivalence can be upgraded to that of ribbon braided quasi-coactions, and then the associated reflection operators (K-matrices) become a tangible invariant of the quantization. As an application we obtain a Kohno–Drinfeld type theorem on type B braid group representations defined by the monodromy of KZ-equations and by the Balagović–Kolb universal K-matrices. The cases of Hermitian and non-Hermitian symmetric spaces are significantly different. In particular, in the latter case a quasi-coaction is essentially uniq

• Christensen, Johannes & Neshveyev, Sergey (2022). (Non)exotic completions of the group algebras of isotropy groups. International Mathematics Research Notices (IMRN). ISSN 1073-7928. 2022(19), s. 15155–15186. doi: 10.1093/imrn/rnab127. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by the problem of characterizing KMS states on the reduced C∗-algebras of étale groupoids, we show that the reduced norm on these algebras induces a C∗-norm on the group algebras of the isotropy groups. This C∗-norm coincides with the reduced norm for the transformation groupoids, but, as follows from examples of Higson–Lafforgue–Skandalis, it can be exotic already for groupoids of germs associated with group actions. We show that the norm is still the reduced one for some classes of graded groupoids, in particular, for the groupoids associated with partial actions of groups and the semidirect products of exact groups and groupoids with amenable isotropy groups.

• Neshveyev, Sergey & Stammeier, Nicolai (2022). The groupoid approach to equilibrium states on right LCM semigroup C*-algebras. Journal of the London Mathematical Society. ISSN 0024-6107. 105(1), s. 220–250. doi: 10.1112/jlms.12510. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Neshveyev, Sergey (2026). Ideal structure of groupoid C*-algebras. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2025). Topological structure of the Mackey machine for etale groupoids. Fulltekst i vitenarkiv
• Kvaal, Simen; Bergan, Snorre; Fredheim, Håkon Richard; Larsen, Nadia S. & Neshveyev, Sergey (2025). A mathematical approach to CC theory. Fulltekst i vitenarkiv Vis sammendrag

  In this talk, I will outline work being carried out in an interdisciplinary project with the Operator Algebra group at Department of Mathematics, UiO. We have done a complete reformulation of coupled-cluster methods from the point of view of the bivariational principle, which gives a more “geometric” view. We have formulated general strategies for a posteriori and a priori error estimation using a nonlinear inf-sup theorem. Several results and proofs are simplified compared to those found in the literature. We are able to place all the analyses presently in the literature in this framework, in particular the seminal works by Rohwedder—Schneider, and Hassan—Maday—Wang

• Neshveyev, Sergey (2024). Cuntz–Pimsner algebras of Temperley–Lieb subproduct systems. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2024). KK-duality and quantum hyperbolicity. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2024). Operator algebras (4 lectures). Fulltekst i vitenarkiv
• Neshveyev, Sergey (2023). Dual cocycles and quantization of a class of locally compact groups. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2023). Faithful representations of reduced groupoid C*-algebras, with application to semigroup C*-algebras. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2022). Subproduct systems with quantum group symmetry. Fulltekst i vitenarkiv
• Neshveyev, Sergey (2022). Subproduct systems, associated C*-algebras and their symmetries (3 lectures). Fulltekst i vitenarkiv

Se alle arbeider i NVA