Positselski, Leonid

This paper is based on the material of Section 4 and Appendix C in arXiv:1503.05523v6, which was excluded from the subsequent versions of arXiv:1503.05523. We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras $\mathcal C$ and $\mathcal D$. Given such a complex $\mathcal B^\bullet$, we ...

Lawton, Sean Sikora, Adam S.

Let G be a connected reductive affine algebraic group. In this short note we define the "variety of G-characters" of a finitely generated group F and show that the quotient of the G-character variety of F by the action of the trace preserving outer automorphisms of G normalizes the variety of G-characters when F is a free group, free abelian group,...

Guo, Jin Yun Luo, Deren

In this paper we study a class of algebras having $n$-dimensional pyramid shaped quiver with $n$-cubic cells, which we called $n$-cubic pyramid algebras. This class of algebras includes the quadratic dual of the basic $n$-Auslander absolutely $n$-complete algebras introduced by Iyama. We show that the projective resolution of the simples of $n$-cub...

Ovsienko, Valentin Tabachnikov, Serge

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Bouarroudj, Sofiane Krutov, Andrey Leites, Dimitry Shchepochkina, Irina

We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with non-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebras of vector fields with polynomial coefficients, (d) string...

Kobayashi, Toshiyuki Nasrin, Salma

Consider the restriction of an irreducible unitary representation $\pi$ of a Lie group $G$ to its subgroup $H$. Kirillov's revolutionary idea on the orbit method suggests that the multiplicity of an irreducible $H$-module $\nu$ occurring in the restriction $\pi|_H$ could be read from the coadjoint action of $H$ on $O^G \cap pr^{-1}(O^H)$ provided $...

Ginzburg, Victor Rozenblyum, Nick
Published in
Algebras and Representation Theory

Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplec...

Grimley, Lauren Uhl, Christine

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...