Inner actions of weak Hopf algebras-Reference-Cited by-同舟云学术

Inner actions of weak Hopf algebras

Published:2017-04-12 Issue:06 Volume:16 Page:1750118
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Bagio Dirceu¹,Flôres Daiana¹,Sant’ana Alveri²

Affiliation:

1. Departamento de Matemática, Universidade Federal de Santa Maria, Brazil

2. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Brazil

Abstract

Let [Formula: see text] be an associative ring and [Formula: see text] idempotent elements of [Formula: see text]. In this paper we introduce the notion of [Formula: see text]-invertibility for an element of [Formula: see text] and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra [Formula: see text] and an algebra [Formula: see text], we present sufficient conditions for [Formula: see text] to admit an inner action of [Formula: see text]. We also prove that if [Formula: see text] is a left [Formula: see text]-module algebra then [Formula: see text] acts innerly on the smash product [Formula: see text] if and only if [Formula: see text] is a quantum commutative weak Hopf algebra.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817501183

Reference11 articles.

1. STRONGLY $\pi$-REGULAR RINGS

2. Crossed products and inner actions of Hopf algebras

3. Weak Hopf Algebras

4. SIMPLE REGULAR SKEW GROUP RINGS

5. Pseudo-Inverses in Associative Rings and Semigroups

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