IRREDUCIBLE ACTIONS AND COMPRESSIBLE MODULES

• Type: Article in International Scientific Journal
• Date: 2011

Authors

borges, ines (Author) Other; lomp, christian (Author) Other

Journal

Title: Journal of Algebra and its Applications

Pages: 101-117

ISSN: 0219-4988

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-V8B

DOI: 10.1142/S0219498811004446

Abstract (EN): Any finite set of linear operators on an algebra A yields an operator algebra B and a module structure on A, whose endomorphism ring is isomorphic to a subring A(B) of certain invariant elements of A. We show that if A is a critically compressible left B-module, then the dimension of its self-injective hull (A) over cap over the ring of fractions of A(B) is bounded by the uniform dimension of A and the number of linear operators generating B. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions.

Language: English

Type (Professor's evaluation): Scientific