Actions of Taft's algebras on finite dimensional algebras

Author(s)

Centrone, Lucio ^{[1, 2]} ; Yasumura, Felipe ^[3]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Bari Aldo Moro, Campus Univ Ernesto Quagliarello, Via E Orabona 4, I-70125 Bari - Italy

^[3] Univ Sao Paulo, Inst Matemat & Estat, Dept Math, Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Algebra; v. 560, p. 725-744, OCT 15 2020.
• Web of Science Citations: 0

Abstract

Let F be a field containing a primitive m-th root of the unit. We characterize the actions of a Taft's algebra H-m of a certain order m on finite dimensional arbitrary algebras. We describe the action in terms of gradings and actions by skew-derivations. Moreover we prove the associative algebra UT2 of 2 x 2 upper triangular matrices with entries from F does not generate a variety of H-m-module algebras of almost polynomial growth. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/02108-7 - Identities in (non) associative algebras and related themes.
• Grantee: Lucio Centrone
• Support Opportunities: Regular Research Grants