2015/11/07 by Lars Kadison, Kadison, Lars
Mathematics · #16D20 #16D90 #16T05 #18D10 #20C05 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:16D20 #msc:16D90 #msc:16T05 #msc:18D10 #msc:20C05
paper · pdf · doi:10.48550/arxiv.1511.02349
27 pp, dedication, additional acknowledgements, and grammatical corrections
arxiv created 2015/11/27 · arxiv updated 2015/11/30
Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary Frobenius extension. We study the core Hopf ideal of a Hopf subalgebra, noting that the length of the annihilator chain of tensor powers of the quotient module is linearly related to the depth, if the Hopf algebra is semisimple. A tensor categorical definition of depth is introduced, and a summary from this new point of view of previous results are included. It is shown in a last section that the depth, Bratteli diagram and relative cyclic homology of algebra extensions are Morita invariants.