Maschke’s theorem for smash products of quasitriangular weak Hopf algebras

Autor:	Wen-juan Zhai, Liang-yun Zhang
Rok vydání:	2011
Předmět:	Discrete mathematics Quantum group General Mathematics Mathematics::Rings and Algebras Field (mathematics) Hopf algebra Quasitriangular Hopf algebra Number theory Differential geometry Mathematics::Category Theory Mathematics::Quantum Algebra Maschke's theorem Commutative property Mathematics
Zdroj:	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 81:35-44
ISSN:	1865-8784 0025-5858
DOI:	10.1007/s12188-010-0047-7
Popis:	The paper is concerned with the semisimplicity of smash products of quasitriangular weak Hopf algebras. Let (H,R) be a finite dimensional quasitriangular weak Hopf algebra over a field k and A any semisimple and quantum commutative weak H-module algebra. Based on the work of Nikshych et al. (Topol. Appl. 127(1–2):91–123, 2003), we give Maschke’s theorem for smash products of quasitriangular weak Hopf algebras, stating that A#H is semisimple if and only if A is a projective left A#H-module, which extends the Theorem 3.2 given in Yang and Wang (Commun. Algebra 27(3):1165–1170, 1999).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::aeb54d59436319a223624651b73e09cd https://doi.org/10.1007/s12188-010-0047-7 Zobrazit plný text záznamu Full text from SpringerLink