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Research papers

1. Quantum Markov K-systems, Mat. Fiz. Anal. Geom. 5 (1998), 87-94 (in Russian).

2. Non-Bernoullian quantum K-systems, Comm. Math. Phys. 195 (1998), 213-232 (joint with V.Ya. Golodets). [pdf]

3. Gibbs states for AF algebras, J. Math. Phys. 39 (1998), 6329-6344 (joint with V.Ya. Golodets). [pdf]

4. On the K-property of quantized Arnold cat maps, J. Math. Phys. 41 (2000), 1961-1965. [pdf]

5. The variational principle for a class of asymptotically abelian C*-algebras, Comm. Math. Phys. 215 (2000), 177-196 (joint with E. Størmer). [pdf]

6. Dynamical entropy for Bogoliubov actions of torsion-free abelian groups on the CAR-algebra, Ergod. Th. & Dynam. Sys. 20 (2000), 1111-1125 (joint with V.Ya. Golodets). [pdf]

7. Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free states, Rev. Math. Phys. 13 (2001), 29-50. [pdf]

8. Entropy of automorphisms of II1-factors arising from the dynamical systems theory, J. Func. Anal. 181 (2001), 14-28 (joint with V.Ya. Golodets). [pdf]

9. Entropy in type I algebras, Pacific J. Math. 201 (2001), 421-428 (joint with E. Størmer). [pdf]

10. Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem, Proc. Amer. Math. Soc. 130 (2002), 2999-3003. [pdf]

11. The McMillan theorem for a class of asymptotically abelian C*-algebras, Ergod. Th. & Dynam. Sys. 22 (2002), 889-897 (joint with E. Størmer). [pdf]

12. Ergodic theory and maximal abelian subalgebras of the hyperfinite factor, J. Func. Anal. 195 (2002), 239-261 (joint with E. Størmer). [pdf]

13. The Martin boundary of a discrete quantum group, J. Reine Angew. Math. 568 (2004), 23-70 (joint with L. Tuset). [pdf]

14. Hopf algebra equivariant cyclic cohomology, K-theory and index formulas, K-Theory 31 (2004), 357-378 (joint with L. Tuset). [pdf]

15. KMS states of quasi-free dynamics on Pimsner algebras, J. Funct. Anal. 211 (2004), 457-482 (joint with M. Laca). [pdf]

16. A local index formula for the quantum sphere, Comm. Math. Phys. 254 (2005), 323-341 (joint with L. Tuset). [pdf]

17. Poisson boundary of the dual of SUq(n), Comm. Math. Phys. 262 (2006), 505-531 (joint with M. Izumi and L. Tuset). [pdf]

18. Phase transition in the Connes-Marcolli GL2-system, J. Noncommut. Geom. 1 (2007), 397-430 (joint with M. Laca and N.S. Larsen). [pdf]

19. Hecke algebras of semidirect products and the finite part of the Connes-Marcolli C*-algebra, Adv. in Math. 217 (2008), 449-488 (joint with M. Laca and N.S. Larsen). [pdf]

20. The ratio set of the harmonic measure of a random walk on a hyperbolic group, Israel J. Math. 163 (2008), 285-316 (joint with M. Izumi and R. Okayasu). [pdf]

21. On Bost-Connes type systems for number fields, J. Number Theory 129 (2009), 325-338 (joint with M. Laca and N.S. Larsen). [pdf]

22. On the definition of L2-Betti numbers of equivalence relations, Internat. J. Algebra Comput. 19 (2009), 383-396 (joint with S. Rustad). [pdf]

23. The Dirac operator on compact quantum groups, J. Reine Angew. Math. 641 (2010), 120 (joint with L. Tuset). [pdf]

24. Twisted cyclic theory, equivariant KK theory and KMS states, J. Reine Angew. Math. 650 (2011), 161191 (joint with A.L. Carey, R. Nest and A. Rennie). [pdf]

25. Symmetric invariant cocycles on the duals of q-deformations, Adv. in Math. 227 (2011), 146-169 (joint with L. Tuset). [pdf]

26. Von Neumann algebras arising from Bost-Connes type systems, Int. Math. Res. Notices. 2011, no. 1, 217-236. [pdf]

27. Type III1 equilibrium states of the Toeplitz algebra of the affine semigroup over the natural numbers, J. Funct. Anal. 261 (2011), 169-187 (joint with M. Laca). [pdf]

28. On second cohomology of duals of compact groups, Intern. Journ. of Math. 22 (2011), no. 9, 1231-1260 (joint with L. Tuset). [pdf]

29. K-homology class of the Dirac operator on a compact quantum group, Documenta Mathematica 16 (2011), 767-780 (joint with L. Tuset). [pdf]

30. Quantized algebras of functions on homogeneous spaces with Poisson stabilizers, Comm. Math. Phys. 312 (2012), no. 1, 223-250 (joint with L. Tuset). [pdf]

31. Autoequivalences of the tensor category of Uqg-modules, Int. Math. Res. Not. IMRN 2012, no. 15, 3498-3508 (joint with L. Tuset). [pdf]

32. Bost-Connes systems, Hecke algebras, and induction, J. Noncommut. Geom. 7 (2013), no. 2, 525-546 (joint with M. Laca and M. Trifkovic). [pdf]

33. On uniqueness of arithmetic models. [pdf] This is appendix to the paper On Endomotives, Lambda-rings and Bost-Connes systems by Bora Yalkinoglu, Invent. Math. 191 (2013), no. 2, 383-425. [arXiv]

34. Deformation of operator algebras by Borel cocycles, J. Funct. Anal. 265 (2013), no. 6, 983-1001 (joint with J. Bhowmick and A. Sangha). [pdf]

35. KMS states on the C*-algebras of non-principal groupoids, J. Operator Theory 70 (2013), no. 2, 513-530. [pdf]

36. Bost-Connes systems associated with function fields, J. Noncommut. Geom. 8 (2014), no. 1, 275-301 (joint with S. Rustad). [pdf]

37. Smooth crossed products of Rieffel's deformations, Lett. Math. Phys. 104 (2014), no. 3, 361-371. [pdf]

38. Deformation of C*-algebras by cocycles on locally compact quantum groups, Adv. Math. 254 (2014), 454-496 (joint with L. Tuset). [pdf]

39. Ergodicity of the action of K* on AK, Int. Math. Res. Not. IMRN 2014, no. 18, 5165-5186 (joint with J.C. Lagarias). [pdf]

40. Duality theory for nonergodic actions, Münster J. Math. 7 (2014), no. 2, 413-437. [pdf]

41. Categorical duality for Yetter-Drinfeld algebras, Doc. Math. 19 (2014), 1105-1139 (joint with M. Yamashita). [pdf]

42. Twisting the q-deformations of compact semisimple Lie groups, J. Math. Soc. Japan 67 (2015), no. 2, 637-662 (joint with M. Yamashita). [pdf]

43. Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras, Transform. Groups 20 (2015), no. 3, 725-742 (joint with K. De Commer). [pdf]

44. Von Neumann algebras of strongly connected higher-rank graphs, Math. Ann. 363 (2015), no. 1-2, 657-678 (joint with M. Laca, N.S. Larsen, A. Sims and S.B.G. Webster). [pdf]

45. On deformations of C*-algebras by actions of Kählerian Lie groups, Internat. J. Math. 27 (2016), no. 3, 1650023 (joint with P. Bieliavsky, V. Gayral and L. Tuset). [pdf]

46. Poisson boundaries of monoidal categories, preprint 2014 (joint with M. Yamashita). [pdf]

47. Classification of non-Kac compact quantum groups of SU(n) type, preprint 2014 (joint with M. Yamashita). [pdf]

48. Drinfeld center and representation theory for monoidal categories, preprint 2015 (joint with M. Yamashita). [pdf]

49. Graded twisting of categories and quantum groups by group actions, preprint 2015 (joint with J. Bichon and M. Yamashita). [pdf]

50. A few remarks on the tube algebra of a monoidal category, preprint 2015 (joint with M. Yamashita). [pdf]

51. Graded twisting of comodule algebras and module categories, preprint 2016 (joint with J. Bichon and M. Yamashita). [pdf]

Announcements, proceedings, etc.

1. Non-isomorphic quantum K-systems of type III1, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 10 (1998), 12-15 (joint with V.Ya. Golodets).

2. Dynamical entropy and quantum K-systems, International Symposium on Mathematical and Theoretical Physics (Kyiv, 1997), Ukrain. Fiz. Zh. 43 (1998), 688-696 (joint with V.Ya. Golodets).

3. Maximal abelian subalgebras of the hyperfinite factor, entropy and ergodic theory, Proceedings of International Workshop on Operator Algebras and Operator Theory (Shanxi, 2001), Acta Math. Sin. (Engl. Ser.) 19 (2003), 599-604 (joint with E. Størmer). [pdf]

4. Quantum random walks and their boundaries, Analysis of (Quantum) Group Actions on Operator Algebras (Kyoto, 2003), RIMS Kokyuroku 1332 (2003), 57-70 (joint with L. Tuset). [pdf]

5. Noncommutative boundaries of q-deformations, Recent Developments on Classification Problems in Operator Algebras (Kyoto, 2005), RIMS Kokyuroku 1435 (2005), 44-52. [pdf]

6. Operator Algebras. The Abel Symposium 2004. Proceedings of the First Abel Symposium, Oslo, September 3-5, 2004, Abel Symposia , Vol. 1, Springer, 2006 (editor, joint with O. Bratteli and C. Skau).

7. Quantizations of Poisson Lie groups as noncommutative manifolds, in: Proceedings of the XVI International Congress on Mathematical Physics, World Scientific, 2010, 504-508 (joint with L. Tuset). [pdf]

8. Notes on the Kazhdan-Lusztig theorem on equivalence of the Drinfeld category and the category of Uq(g)-modules, Algebr. Represent. Theory 14 (2011), 897-948 (joint with L. Tuset). [pdf]

9. Towards a classification of compact quantum groups of Lie type, preprint 2016 (joint with M. Yamashita). [pdf]

Retired preprints

1. Traces on crossed products, preprint 2010. [pdf])

2. Poisson boundaries, Yetter-Drinfeld algebras, and classification of non-Kac compact quantum groups of SU(n) type, preprint 2013 (joint with M. Yamashita). [pdf]

Last modified: 24.05.2016
Books
S. Neshveyev, E. Størmer. Dynamical Entropy in Operator Algebras. A Series of Modern Surveys in Mathematics, Vol. 50. Springer, 2006.
S. Neshveyev, L. Tuset. Compact Quantum Groups and Their Representation Categories. Specialized Courses, Vol. 20. SMF, 2013. Preliminary version: [pdf]