A Mackey decomposition theorem and cohomology for quantum groups at roots of 1
type: Item
instance of: scholarly article
title: A Mackey decomposition theorem and cohomology for quantum groups at roots of 1
zbMATH Open document ID: 0810.17005
published in: Journal of Algebra
publication date: 1994-08-16T00:00:00Z
review text: The author proves a special Mackey decomposition theorem over a field for quantum groups. Using this theorem, he studies the structure of \(R^ 1 \text{ Ind}^ U_{U^{\leq 0} \leq 0}\lambda\) and the nonvanishing property of certain \(R^ i \text{ Ind}^ U_{U^{\leq 0} \leq 0} \lambda\). Moreover, he studies the good filtration of \(U\)-modules and gets a theorem for quantum groups at roots of 1, which describes all composition factors of \(\text{Ind}^ U_{U^{\leq 0} \leq 0} \lambda\) and was first proved for algebraic groups by the reviewer, where \(U\) is the quantum enveloping algebra and \(U^{\leq 0}\) is its subalgebra.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 614253
zbMATH Keywords: cohomology
zbMATH Keywords: Mackey decomposition
zbMATH Keywords: quantum groups
zbMATH Keywords: composition factors
zbMATH Keywords: quantum enveloping algebra
author: Zongzhu Lin
MaRDI profile type: Publication
full work available at URL: jabr.1994.1143
OpenAlex ID: W2003815426
DOI: 10.1006/JABR.1994.1143
description: scientific article; zbMATH DE number 614253