8 papers
Hecke monoids, their homomorphisms and parabolicity
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
We study homomorphisms of Hecke monoids, notably parabolic homomorphisms, which map parabolic elements to parabolic elements, and injective ones. The importance of the first class…
Artin monoids, their homomorphisms and twins
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
Motivated by the twin homomorphism problem for Coxeter groups and the corresponding Hecke monoids, we find a large class of its solutions originating from standard homomorphisms of…
Monomial bialgebras
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permu…
Valuations, bijections, and bases
Arkady Berenstein, Dima Grigoriev
The aim of this paper is to build a theory of commutative and noncommutative {\it injective} valuations of various algebras (including algebras with zero divisors). The targets of…
Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
Arkady Berenstein, Min Huang, Vladimir Retakh
The aim of the paper is to define noncommutative cluster structure on several algebras related to marked surfaces possibly with orbifold points of various orders, wh…
Generalized electrical Lie algebras
Arkady Berenstein, Azat Gainutdinov, Vassily Gorbounov
We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra we associate two types (vertex t…