Professor of Mathematics in the Mathematics Department of University of Oregon “working in representation theory, quantum groups, Schubert calculus, combinatorics, commutative and noncommutative algebraic geometry”.
Oringinal discussion of cluster algebras:
and introducing quantum cluster algebras:
See also:
D. Alessandrini, A. Berenstein, V. Retakh, E. Rogozinnikov, A. Wienhard, Symplectic groups over noncommutative algebras Sel. Math. New Ser. 28, 82 (2022) doi
A. Berenstein, J. Greenstein, Canonical bases of quantum Schubert cells and their symmetries, Sel. Math. New Ser. 23, 2755–2799 (2017) doi
Yuri Bazlov, Arkady Berenstein, Noncommutative Dunkl operators and braided Cherednik algebras, Selecta Math. (N.S.) 14 (2009), no. 3-4, 325–372 pdf, MR2010k:16044 doi
Yuri Bazlov, Arkady Berenstein, Braided doubles and rational Cherednik algebras, Adv. Math. 220 (2009) 1466–1530 doi
We introduce and study a large class of algebras with triangular decomposition which we call braided doubles. Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. We classify braided doubles in terms of quasi-Yetter–Drinfeld (QYD) modules over Hopf algebras which turn out to be a generalisation of the ordinary Yetter-Drinfeld modules. To each braiding (a solution to the braid equation) we associate a QYD-module and the corresponding braided Heisenberg double–this is a quantum deformation of the Weyl algebra where the role of polynomial algebras is played by Nichols-Woronowicz algebras. Our main result is that any rational Cherednik algebra canonically embeds in the braided Heisenberg double attached to the corresponding complex reflection group.
Last revised on July 8, 2024 at 15:48:41. See the history of this page for a list of all contributions to it.