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- Title
Inner actions of weak Hopf algebras.
- Authors
Bagio, Dirceu; Flôres, Daiana; Sant'ana, Alveri
- Abstract
Let be an associative ring and idempotent elements of . In this paper we introduce the notion of -invertibility for an element of and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra and an algebra , we present sufficient conditions for to admit an inner action of . We also prove that if is a left -module algebra then acts innerly on the smash product if and only if is a quantum commutative weak Hopf algebra.
- Subjects
HOPF algebras; ALGEBRAIC topology; IDEMPOTENTS; LINEAR algebra; MATHEMATICAL physics
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 6, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501183