Moscow Mathematical Journal
Volume 21, Issue 2, April–June 2021 pp. 427–442.
Representations of Finite-Dimensional Quotient Algebras of the 3-String Braid Group
We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. If $p=2,3,4,5$, these quotient algebras are finite dimensional. We give semisimplicity criteria for these algebras and present explicit formulas for all their irreducible representations. 2020 Math. Subj. Class. 20F36, 16D60, 20C08
Authors:
Pavel Pyatov (1) and Anastasia Trofimova (2)
Author institution:(1) National Research University Higher School of Economics
20 Myasnitskaya street, Moscow 101000, Russia
Bogoliubov Laboratory of Theoretical Physics, Joint Institute
for Nuclear Research, 141980 Dubna, Moscow Region, Russia
(2) National Research University Higher School of Economics
20 Myasnitskaya street, Moscow 101000, Russia
Center for Advanced Studies, Skolkovo Institute of Science and Technology,
Moscow, Russia
Summary:
Keywords: Braid group, irreducible representations, semisimplicity.
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