Flaut, Cristina
Published in
Algebras and Representation Theory

In this paper, we improve the level and sublevel of algebras obtained by the Cayley-Dickson process when their level and sublevel are greater than the dimension of these algebras.

Chapoton, Frédéric Rognerud, Baptiste
Published in
Algebras and Representation Theory

In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type. When the Coxeter group is a reducible group of type A13\documentclass[12pt]{mi...

Kim, Dongkwan
Published in
Algebras and Representation Theory

We describe Springer fibers corresponding to the minimal and minimal special nilpotent orbits of simple Lie algebras. As a result, we give an answer to the conjecture of Humphreys regarding some graphs attached to Springer fibers.

Garver, Alexander McConville, Thomas
Published in
Algebras and Representation Theory

The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite potential, the exchange graph admits a natural acyclic orientation called the oriented exchange graph, as shown by Brüstle and Yang. The oriented exchange graph is isomorphic ...

Kazhdan, David Ziegler, Tamar
Published in
Algebras and Representation Theory

Let V be a vector space over a field k, P : V → k, d ≥ 3. We show the existence of a function C(r, d) such that rank(P) ≤ C(r, d) for any field k, char(k) > d, a finite-dimensional k-vector space V and a polynomial P : V → k of degree d such that rank(∂P/∂t) ≤ r for all t ∈ V − 0. Our proof of this theorem is based on the application of results on ...

Paradan, Paul-Emile
Published in
Algebras and Representation Theory

In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.

Lu, Ming
Published in
Algebras and Representation Theory

For given bound quiver algebras A and B, we obtain a new algebra Λ, called the simple gluing algebra, by identifying two vertices. We investigate the Gorenstein homological property, the singularity category, the Gorenstein defect category and the Cohen-Macaulay Auslander algebra of Λ in terms of that of A and B. Finally, we give applications to cl...

Zelikson, Shmuel
Published in
Algebras and Representation Theory

Let 𝔤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {g}$\end{document} be a simple complex Lie algebra of types An, Dn, En, and Q a quiver obtained by orienti...

Kleppe, Jan O. Miró-Roig, Rosa M.
Published in
Algebras and Representation Theory

This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...

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

Let Dn,m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {D}_{n,m}$\end{document} be the algebra of quantum integrals of the deformed Calogero-Moser-Sutherland p...