Grimley, Lauren Uhl, Christine
Published in
Algebras and Representation Theory

We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke algebras. We give the necessary and sufficient conditions for which these algebras occur, using Bergman’s Diam...

Molchanov, V. F.
Published in
Algebras and Representation Theory

We construct polynomial quantization (a variant of quantization in the spirit of Berezin) on para-Hermitian symmetric spaces. For that we use two approaches: (a) using a reproducing function, (b) using an “overgroup”. Also we show that the multiplication of symbols is an action of an overalgebra.

Barreiro, Elisabete Kaygorodov, Ivan Sánchez, José M.
Published in
Algebras and Representation Theory

We study the structure of certain k-modules 𝕍 over linear spaces 𝕎 with restrictions neither on the dimensions of 𝕍 and 𝕎 nor on the base field 𝔽. A basis 𝔅={vi}i∈I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setleng...

Giannelli, Eugenio Law, Stacey Martin, Stuart
Published in
Algebras and Representation Theory

Let p be a prime number. In this article we study the restriction to 𝔖n−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {S}_{n-1}$\end{document} of irreducibl...

Bagci, Irfan Calixto, Lucas Macedo, Tiago
Published in
Algebras and Representation Theory

Given an algebraically closed field 𝕜 of characteristic zero, a Lie superalgebra 𝔤 over 𝕜 and an associative, commutative 𝕜-algebra A with unit, a Lie superalgebra of the form 𝔤 ⊗𝕜A is known as a map superalgebra. Map superalgebras generalize important classes of Lie superalgebras, such as, loop superalgebras (where A = 𝕜[t±1]), and current superal...

Panov, A. N.
Published in
Algebras and Representation Theory

A supercharacter theory is constructed for the parabolic subgroups of the group GL(n, Fq) with blocks of orders less or equal to two. The author formulated the hypotheses on construction of a supercharacter theory for an arbitrary parabolic subgroup in GL(n, Fq).

Yildirim, Emine
Published in
Algebras and Representation Theory

Let J(C) be the poset of order ideals of a cominuscule poset C where C comes from two of the three infinite families of cominuscule posets or the exceptional cases. We show that the Auslander-Reiten translation τ on the Grothendieck group of the bounded derived category for the incidence algebra of the poset J(C), which is called the Coxeter transf...

Millionshchikov, Dmitry
Published in
Algebras and Representation Theory

We discuss the notion of characteristic Lie algebra of a hyperbolic PDE. The integrability of a hyperbolic PDE is closely related to the properties of the corresponding characteristic Lie algebra χ. We establish two explicit isomorphisms: the first one is between the characteristic Lie algebra χ(sinhu)\documentclass[12pt]{minimal} \usepackage{amsma...

Etingof, Pavel Neshveyev, Sergey
Published in
Algebras and Representation Theory

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie algebras.

Guccione, Jorge A. Guccione, Juan J. Valqui, Christian
Published in
Algebras and Representation Theory

We introduce the notion of non-degenerate solution of the braid equation on the incidence coalgebra of a locally finite order. Each one of these solutions induces by restriction a non-degenerate set-theoretic solution over the underlying set. So, it makes sense to ask if a non-degenerate set-theoretic solution on the underlying set of a locally fin...