nLab Arkady Berenstein

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 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.

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

category: people