Hall polynomials for tame quivers with automorphism
type: Item
instance of: scholarly article
title: Hall polynomials for tame quivers with automorphism
zbMATH Open document ID: 1498.16019
author: Bangming Deng
author: Lina Han
published in: Journal of Algebra
publication date: 2022-02-14T00:00:00Z
review text: Classical Hall polynomials play important roles in the study of representations of symmetric groups and general linear groups. They are defined by counting certain subgroups of finite abelian \(p\)-groups, which are closely connected to Hall-Littlewood functions. Let \(Q\) be a tame quiver with automorphism \(\sigma\). The pair \((Q,\sigma)\) defines a family of tame hereditary algebras \(\mathfrak{U}(Q,\sigma;q)\) over a finite field \(\mathbb{F}_q\) of \(q\) elements. The authors prove that Hall polynomial exists for each triple of decomposition sequences associated with tame quivers with automorphism \(\mathfrak{U}(Q,\sigma;q)\) (Theorem 3.6, page 228).
reviewed by: Mee Seong Im
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7473021
zbMATH Keywords: Ringel-Hall algebra
zbMATH Keywords: Hall polynomial
zbMATH Keywords: tame quiver with automorphism
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2021.12.039
OpenAlex ID: W4206372692
cites work: Q5704250
cites work: Q5686079
cites work: Decomposition classes of representations of tame quivers.
cites work: Generalized Kac-Moody algebras
cites work: Q4676821
cites work: Frobenius morphisms and representations of algebras
cites work: Q3416323
cites work: Q3539474
cites work: Hall polynomials for tame type
cites work: Indecomposable representations of graphs and algebras
cites work: Q4189399
cites work: Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
cites work: Hall algebras, hereditary algebras and quantum groups
cites work: The hall polynomials of a cyclic serial algebra
cites work: Universal PBW-bases of Hall-Ringel algebras and Hall polynomials
cites work: Q5733585
cites work: Hall polynomials for affine quivers
cites work: Q4040877
cites work: Q4399987
cites work: Some Hall polynomials for representation-finite trivial extension algebras
cites work: Lie algebras generated by indecomposables
cites work: Hall algebras and quantum groups
cites work: Q3972806
cites work: Hall polynomials for the representation-finite hereditary algebras
cites work: The Composition Algebra of a Cyclic Quiver
cites work: Hall numbers and the composition algebra of the Kronecker algebra.
cites work: On some Ringel-Hall products in tame cases.
cites work: Composition algebras of affine type
cites work: PBW-basis for the composition algebra of the Kronecker algebra
DOI: 10.1016/J.JALGEBRA.2021.12.039
description: scientific article; zbMATH DE number 7473021