Professor Xin Li

  • Chair of Mathematical Analysis (Mathematics)

Research interests

Research Interests

I am working on C*-algebras and their connections to other mathematical disciplines such as topological dynamics, group theory or number theory. My research interests include semigroup C*-algebras, K-theory, Cartan subalgebras of C*-algebras, continuous orbit equivalence, and topological full groups.

Research Groups


Publications

List by: Type | Date

Jump to: 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010
Number of items: 32.

2020

Li, X. , Omland, T. and Spielberg, J. (2020) C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics, (doi: 10.1007/s00220-020-03758-5) (Early Online Publication)

Li, X. (2020) Every classifiable simple C*-algebra has a Cartan subalgebra. Inventiones Mathematicae, 219(2), pp. 653-699. (doi: 10.1007/s00222-019-00914-0)

Barlak, S. and Li, X. (2020) Cartan subalgebras and the UCT problem, II. Mathematische Annalen, (Accepted for Publication)

2019

Li, X. (2019) K-theory for generalized Lamplighter groups. Proceedings of the American Mathematical Society, 147(10), pp. 4371-4378. (doi: 10.1090/proc/14619)

Li, X. and Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372(3), pp. 1985-2010. (doi: 10.1090/tran/7654)

Cornelissen, G., Li, X. , Marcolli, M. and Smit, H. (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25(2), 24. (doi: 10.1007/s00029-019-0469-8)

Cornelissen, G., de Smit, B., Li, X. , Marcolli, M. and Smit, H. (2019) Characterization of global fields by Dirichlet L-series. Research in Number Theory, 5(1), 7. (doi: 10.1007/s40993-018-0143-9)

2018

Chu, C.-H. and Li, X. (2018) Amenability, Reiter's condition and Liouville property. Journal of Functional Analysis, 274(12), pp. 3291-3324. (doi: 10.1016/j.jfa.2018.03.014)

Li, X. (2018) Continuous orbit equivalence rigidity. Ergodic Theory and Dynamical Systems, 38(4), pp. 1543-1563. (doi: 10.1017/etds.2016.98)

2017

Cuntz, J., Echterhoff, S., Li, X. and Yu, G. (Eds.) (2017) K-Theory for Group C*-Algebras and Semigroup C*-Algebras. Series: Oberwolfach seminars. Birkhäuser: Cham, Switzerland. ISBN 9783319599144

Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017(17), pp. 5233-5259. (doi: 10.1093/imrn/rnw166)

Barlak, S. and Li, X. (2017) Cartan subalgebras and the UCT problem. Advances in Mathematics, 316, pp. 748-769. (doi: 10.1016/j.aim.2017.06.024)

2016

Li, X. (2016) Semigroup C*-Algebras. In: Abel Symposium 2015, Coastal Express (Hurtigruten), Norway, 07-11 Aug 2015, pp. 191-202. ISBN 9783319392844 (doi:10.1007/978-3-319-39286-8_9)

Li, X. (2016) Semigroup C*-algebras of ax + b-semigroups. Transactions of the American Mathematical Society, 368(6), pp. 4417-4437. (doi: 10.1090/tran/6469)

Li, X. (2016) On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, 291, pp. 1-11. (doi: 10.1016/j.aim.2015.12.024)

Li, X. and Norling, M. D. (2016) Independent resolutions for totally disconnected dynamical systems. II. C*-algebraic case. Journal of Operator Theory, 75(1), pp. 163-193. (doi: 10.7900/jot.2014dec22.2061)

Eilers, S., Li, X. and Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

2015

Li, X. (2015) A new approach to recent constructions of C*-algebras from modular index theory. Journal of Functional Analysis, 269(3), pp. 841-864. (doi: 10.1016/j.jfa.2014.12.015)

Li, X. and Norling, M. D. (2015) Independent resolutions for totally disconnected dynamical systems I: algebraic case. Journal of Algebra, 424, pp. 98-125. (doi: 10.1016/j.jalgebra.2014.10.043)

Cuntz, J., Echterhoff, S. and Li, X. (2015) On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. Journal of the European Mathematical Society, 17(3), pp. 645-687. (doi: 10.4171/JEMS/513)

2014

Li, X. (2014) On K-theoretic invariants of semigroup C*-algebras attached to number fields. Advances in Mathematics, 264, pp. 371-395. (doi: 10.1016/j.aim.2014.07.014)

2013

Li, X. (2013) Nuclearity of semigroup C*-algebras and the connection to amenability. Advances in Mathematics, 244, pp. 626-662. (doi: 10.1016/j.aim.2013.05.016)

Cuntz, J., Echterhoff, S. and Li, X. (2013) On the k-Theory of crossed products by automorphic semigroup actions. Quarterly Journal of Mathematics, 64(3), pp. 747-784. (doi: 10.1093/qmath/hat021)

Larsen, N. S. and Li, X. (2013) Dilations of semigroup crossed products as crossed products of dilations. Proceedings of the American Mathematical Society, 141(5), pp. 1597-1603. (doi: 10.1090/S0002-9939-2013-11475-9)

2012

Li, X. and Lück, W. (2012) K-theory for ring c*-algebras: the case of number fields with higher roots of unity. Journal of Topology and Analysis, 4(4), pp. 449-479. (doi: 10.1142/S1793525312500203)

Li, X. (2012) K-theory for ring C*-algebras attached to function fields with only one infinite place. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 10(1), pp. 203-231. (doi: 10.1017/is011011023jkt177)

Li, X. (2012) Semigroup C⁎-algebras and amenability of semigroups. Journal of Functional Analysis, 262(10), pp. 4302-4340. (doi: 10.1016/j.jfa.2012.02.020)

Larsen, N. S. and Li, X. (2012) The 2-adic ring C*-algebra of the integers and its representations. Journal of Functional Analysis, 262(4), pp. 1392-1426. (doi: 10.1016/j.jfa.2011.11.008)

2011

Cuntz, J. and Li, X. (2011) C*-algebras associated with integral domains and crossed products by actions on adele spaces. Journal of Noncommutative Geometry, 5(1), pp. 1-37. (doi: 10.4171/JNCG/68)

Cuntz, J. and Li, X. (2011) K-theory for ring C-algebras attached to polynomial rings over finite fields. Journal of Noncommutative Geometry, 5(3), pp. 331-349. (doi: 10.4171/JNCG/78)

2010

Li, X. (2010) Ring C*-algebras. Mathematische Annalen, 348(4), pp. 859-898. (doi: 10.1007/s00208-010-0502-x)

Cuntz, J. and Li, X. (2010) The regular C*-algebra of an integral domain. In: Blanchard, E., Ellwood, D., Khalkhali, M., Marcolli, M., Moscovici, H. and Popa, S. (eds.) Quanta of Maths: Conference in Honor of Alain Connes, Non Commutative Geometry, Institut Henri Poincaré, Institut des Hautes Études Scientifiques, Institut de Mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Series: Clay mathematics proceedings (11). American Mathematical Society ; Clay Mathematics Institute: Providence, R.I ; Cambridge, MA, pp. 149-170. ISBN 9780821852033

This list was generated on Wed Jul 8 14:01:02 2020 BST.
Number of items: 32.

Articles

Li, X. , Omland, T. and Spielberg, J. (2020) C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type. Communications in Mathematical Physics, (doi: 10.1007/s00220-020-03758-5) (Early Online Publication)

Li, X. (2020) Every classifiable simple C*-algebra has a Cartan subalgebra. Inventiones Mathematicae, 219(2), pp. 653-699. (doi: 10.1007/s00222-019-00914-0)

Barlak, S. and Li, X. (2020) Cartan subalgebras and the UCT problem, II. Mathematische Annalen, (Accepted for Publication)

Li, X. (2019) K-theory for generalized Lamplighter groups. Proceedings of the American Mathematical Society, 147(10), pp. 4371-4378. (doi: 10.1090/proc/14619)

Li, X. and Renault, J. (2019) Cartan subalgebras in C*-algebras. Existence and uniqueness. Transactions of the American Mathematical Society, 372(3), pp. 1985-2010. (doi: 10.1090/tran/7654)

Cornelissen, G., Li, X. , Marcolli, M. and Smit, H. (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25(2), 24. (doi: 10.1007/s00029-019-0469-8)

Cornelissen, G., de Smit, B., Li, X. , Marcolli, M. and Smit, H. (2019) Characterization of global fields by Dirichlet L-series. Research in Number Theory, 5(1), 7. (doi: 10.1007/s40993-018-0143-9)

Chu, C.-H. and Li, X. (2018) Amenability, Reiter's condition and Liouville property. Journal of Functional Analysis, 274(12), pp. 3291-3324. (doi: 10.1016/j.jfa.2018.03.014)

Li, X. (2018) Continuous orbit equivalence rigidity. Ergodic Theory and Dynamical Systems, 38(4), pp. 1543-1563. (doi: 10.1017/etds.2016.98)

Li, X. (2017) Partial transformation groupoids attached to graphs and semigroups. International Mathematics Research Notices, 2017(17), pp. 5233-5259. (doi: 10.1093/imrn/rnw166)

Barlak, S. and Li, X. (2017) Cartan subalgebras and the UCT problem. Advances in Mathematics, 316, pp. 748-769. (doi: 10.1016/j.aim.2017.06.024)

Li, X. (2016) Semigroup C*-algebras of ax + b-semigroups. Transactions of the American Mathematical Society, 368(6), pp. 4417-4437. (doi: 10.1090/tran/6469)

Li, X. (2016) On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II. Advances in Mathematics, 291, pp. 1-11. (doi: 10.1016/j.aim.2015.12.024)

Li, X. and Norling, M. D. (2016) Independent resolutions for totally disconnected dynamical systems. II. C*-algebraic case. Journal of Operator Theory, 75(1), pp. 163-193. (doi: 10.7900/jot.2014dec22.2061)

Eilers, S., Li, X. and Ruiz, E. (2016) The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids. Documenta Mathematica, 21, pp. 309-343.

Li, X. (2015) A new approach to recent constructions of C*-algebras from modular index theory. Journal of Functional Analysis, 269(3), pp. 841-864. (doi: 10.1016/j.jfa.2014.12.015)

Li, X. and Norling, M. D. (2015) Independent resolutions for totally disconnected dynamical systems I: algebraic case. Journal of Algebra, 424, pp. 98-125. (doi: 10.1016/j.jalgebra.2014.10.043)

Cuntz, J., Echterhoff, S. and Li, X. (2015) On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. Journal of the European Mathematical Society, 17(3), pp. 645-687. (doi: 10.4171/JEMS/513)

Li, X. (2014) On K-theoretic invariants of semigroup C*-algebras attached to number fields. Advances in Mathematics, 264, pp. 371-395. (doi: 10.1016/j.aim.2014.07.014)

Li, X. (2013) Nuclearity of semigroup C*-algebras and the connection to amenability. Advances in Mathematics, 244, pp. 626-662. (doi: 10.1016/j.aim.2013.05.016)

Cuntz, J., Echterhoff, S. and Li, X. (2013) On the k-Theory of crossed products by automorphic semigroup actions. Quarterly Journal of Mathematics, 64(3), pp. 747-784. (doi: 10.1093/qmath/hat021)

Larsen, N. S. and Li, X. (2013) Dilations of semigroup crossed products as crossed products of dilations. Proceedings of the American Mathematical Society, 141(5), pp. 1597-1603. (doi: 10.1090/S0002-9939-2013-11475-9)

Li, X. and Lück, W. (2012) K-theory for ring c*-algebras: the case of number fields with higher roots of unity. Journal of Topology and Analysis, 4(4), pp. 449-479. (doi: 10.1142/S1793525312500203)

Li, X. (2012) K-theory for ring C*-algebras attached to function fields with only one infinite place. Journal of K-theory: K-theory and its Applications to Algebra, Geometry and Topology, 10(1), pp. 203-231. (doi: 10.1017/is011011023jkt177)

Li, X. (2012) Semigroup C⁎-algebras and amenability of semigroups. Journal of Functional Analysis, 262(10), pp. 4302-4340. (doi: 10.1016/j.jfa.2012.02.020)

Larsen, N. S. and Li, X. (2012) The 2-adic ring C*-algebra of the integers and its representations. Journal of Functional Analysis, 262(4), pp. 1392-1426. (doi: 10.1016/j.jfa.2011.11.008)

Cuntz, J. and Li, X. (2011) C*-algebras associated with integral domains and crossed products by actions on adele spaces. Journal of Noncommutative Geometry, 5(1), pp. 1-37. (doi: 10.4171/JNCG/68)

Cuntz, J. and Li, X. (2011) K-theory for ring C-algebras attached to polynomial rings over finite fields. Journal of Noncommutative Geometry, 5(3), pp. 331-349. (doi: 10.4171/JNCG/78)

Li, X. (2010) Ring C*-algebras. Mathematische Annalen, 348(4), pp. 859-898. (doi: 10.1007/s00208-010-0502-x)

Book Sections

Cuntz, J. and Li, X. (2010) The regular C*-algebra of an integral domain. In: Blanchard, E., Ellwood, D., Khalkhali, M., Marcolli, M., Moscovici, H. and Popa, S. (eds.) Quanta of Maths: Conference in Honor of Alain Connes, Non Commutative Geometry, Institut Henri Poincaré, Institut des Hautes Études Scientifiques, Institut de Mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Series: Clay mathematics proceedings (11). American Mathematical Society ; Clay Mathematics Institute: Providence, R.I ; Cambridge, MA, pp. 149-170. ISBN 9780821852033

Edited Books

Cuntz, J., Echterhoff, S., Li, X. and Yu, G. (Eds.) (2017) K-Theory for Group C*-Algebras and Semigroup C*-Algebras. Series: Oberwolfach seminars. Birkhäuser: Cham, Switzerland. ISBN 9783319599144

Conference Proceedings

Li, X. (2016) Semigroup C*-Algebras. In: Abel Symposium 2015, Coastal Express (Hurtigruten), Norway, 07-11 Aug 2015, pp. 191-202. ISBN 9783319392844 (doi:10.1007/978-3-319-39286-8_9)

This list was generated on Wed Jul 8 14:01:02 2020 BST.