Decomposition of some pointed Hopf algebras given by the canonical Nakayama automorphism

2006/03/15 by M. Graña, Graña, M., J. A. Guccione +3
Mathematics · #16W30 #16W50 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30 #msc:16W50

paper · pdf · doi:10.48550/arxiv.math/0603384

8 pages

arxiv created 2006/03/15 · arxiv updated 2009/12/01

Abstract

Every finite dimensional Hopf algebra is a Frobenius algebra, with Frobenius homomorphism given by an integral. The Nakayama automorphism determined by it yields a decomposition with degrees in a cyclic group. For a family of pointed Hopf algebras, we determine necessary and sufficient conditions for this decomposition to be strongly graded.

Related

• Pointed Hopf algebras and Quasi-isomorphisms
• Nakayama automorphism of a class of graded algebras
• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra
• The action of the Nakayama automorphism of a Frobenius algebra on Hochschild cohomology
• Nakayama automorphism and applications