2012/02/15 by Edson R. Alvares, Alvares, Edson R., Marcelo M. S. Alves +3
Mathematics · #16D90 #16S35 #16S40 #16T05 #18E05 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:16D90 #msc:16S35 #msc:16S40 #msc:16T05 #msc:18E05
paper · pdf · doi:10.48550/arxiv.1202.3343
28 pages
arxiv created 2012/02/15 · arxiv updated 2012/02/16
The effectiveness of the aplication of constructions in G-graded k-categories to the computation of the fundamental group of a finite dimensional k-algebra, alongside with open problems still left untouched by those methods and new problems arisen from the introduction of the concept of fundamental group of a k-linear category, motivated the investigation of H-module categories, i.e., actions of a Hopf algebra H on a k-linear category. The G-graded case corresponds then to actions of the Hopf algebra kG on a k-linear category. In this work we take a step further and introduce partial H-module categories. We extend several results of partial H-module algebras to this context, such as the globalization theorem, the construction of the partial smash product and the Morita equivalence of this category with the smash product over a globalization. We also present a detailed description of partial actions of kG.