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”.

- webpage at Univ. of Oregon; papers
- Arkady Berenstein, Andrei Zelevinsky,
*Quantum cluster algebras*, math.QA/0404446 - 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 ofquasi-Yetter–Drinfeld(QYD)modulesover 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 thebraided Heisenberg doubleattached to the corresponding complex reflection group.

- Arkady Berenstein, Sebastian Zwicknagl,
*Braided symmetric and exterior algebras*, Trans. Amer. Math. Soc. 360 (2008) 3429–3472 doi

category: people

Created on September 22, 2022 at 09:38:32. See the history of this page for a list of all contributions to it.