lucasyh

• Cioletti, L.; Hataishi, Lucas Yudi; Lopes, A.O. & Stadlbauer, M. (2024). Spectral triples and Dixmier trace representations of Gibbs measures: theory and examples. Nonlinearity. ISSN 0951-7715. 37(10). doi: 10.1088/1361-6544/ad7009. Fulltekst i vitenarkiv Vis sammendrag

  In this paper we study spectral triples and non-commutative expectations associated to expanding and weakly expanding maps. In order to do so, we generalise the Perron–Frobenius–Ruelle theorem and obtain a polynomial decay of the operator, which allows to prove differentiability of a dynamically defined ζ-function at its critical parameter. We then generalise Sharp's construction of spectral triples to this setting and provide criteria when the associated spectral metric is non-degenerate and when the non-commutative expectation of the spectral triple is colinear to the integration with respect to the associated equilibrium state from thermodynamic formalism. Due to our general setting, we are able to simultaneously analyse expanding maps on manifolds or connected fractals, subshifts of finite type as well as the Dyson model from statistical physics, which underlines the unifying character of noncommutative geometry. Furthermore, we derive an explicit representation of the ζ-function associated to a particular class of pathological continuous potentials, giving rise to examples where the representation as a non-commutative expectation via the associated zeta function holds, and others where it does not hold.

• Ro, Joeri De & Hataishi, Lucas Yudi (2024). Actions of Compact and Discrete Quantum Groups on Operator Systems. International Mathematics Research Notices (IMRN). ISSN 1073-7928. 2024(15), s. 11190–11220. doi: 10.1093/imrn/rnae118. Fulltekst i vitenarkiv Vis sammendrag

  We introduce the notion of an action of a discrete or compact quantum group on an operator system, and study equivariant operator system injectivity. We then prove a duality result that relates equivariant injectivity with dual injectivity of associated crossed products. As an application, we give a description of the equivariant injective envelope of the reduced crossed product built from an action of a discrete quantum group on an operator system.

• Habbestad, Erik; Hataishi, Lucas Yudi & Neshveyev, Sergey (2022). Noncommutative Poisson boundaries and Furstenberg–Hamana boundaries of Drinfeld doubles. Journal des Mathématiques Pures et Appliquées. ISSN 0021-7824. 159, s. 313–347. doi: 10.1016/j.matpur.2021.12.006. Fulltekst i vitenarkiv

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• Hataishi, Lucas Yudi (2022). Injective Envelopes of C*-module categories. Fulltekst i vitenarkiv
• Hataishi, Lucas Yudi (2022). Injective envelopes of C*-module categories and boundary theory. Fulltekst i vitenarkiv
• Hataishi, Lucas Yudi (2022). Categorification of Yetter-Drinfeld structures. Fulltekst i vitenarkiv
• Hataishi, Lucas Yudi (2022). Yetter-Drinfeld algebras, module categories and injectivity. Fulltekst i vitenarkiv
• Hataishi, Lucas Yudi (2021). Boundary Actions, Drinfeld Doubles and Free Unitary Quantum Groups. Fulltekst i vitenarkiv

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