5 papers · 1 filter
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…
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…
Multiple Horn problems for planar networks and invertible matrices
Anton Alekseev, Arkady Berenstein, Anfisa Gurenkova +1
The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations and for a triple of invertible matrices with giv…
Hecke and Artin monoids and their homomorphisms
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
The aim of the present work is to systematically study homomorphisms of Hecke and Artin monoids and thus to develop their comprehensive theory. Our original motivation was the stri…