Extensions of symmetric tensors by alternating tensors
type: Item
instance of: scholarly article
title: Extensions of symmetric tensors by alternating tensors
zbMATH Open document ID: 0682.14033
DOI: 10.1016/0021-8693(89)90071-9
author: Kaan Akin
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let F be a free module of rank d over a commutative ring R. Let \(\bigwedge^ nF\) and \(D_ nF\) be the n-th homogeneous components of the exterior algebra \(\bigwedge F=\sum \bigwedge^ iF \) and the divided power algebra \(DF=\sum D_ jF \), respectively. The author shows that the extension group \(Ext^ m(\bigwedge^ mF,D_ nF)\) in the category of the polynomial representations of the algebraic group scheme GL(F) over R is isomorphic as an R-module to the homogeneous component in degree \( n\) of the homology module \(H_{n-m}(DG_ a)\) of the hyperalgebra \(DG_ a\) of the algebraic group scheme \(G_ a\) over R. This paper makes an important contribution to representation theory.
Mathematics Subject Classification ID: 14L17
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 4116710
zbMATH Keywords: exterior algebra
zbMATH Keywords: divided power algebra
zbMATH Keywords: polynomial representations of the algebraic group scheme
zbMATH Keywords: hyperalgebra
zbMATH Keywords: representation theory
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90071-9
OpenAlex ID: W1963540981
cites work: Characteristic-free representation theory of the general linear group. II: Homological considerations
cites work: Schur functors and Schur complexes
cites work: Rational and generic cohomology
cites work: On Schur algebras and related algebras. II
cites work: Polynomial representations of \(GL_n\)
cites work: Homology
description: scientific article; zbMATH DE number 4116710