2025/02/21 by Ohara, Mariko
#16T15 #18G20 #55N25 #57T0 #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2502.15191
Let H be a finite dimensional Hopf algebra over a field K. In this paper, we study when an H-extension becomes a tame H-extension by calculating Hopfological homology and Hopf-cyclic homology. In the (derived) category of H'-comodules for a Hopf algebra H', we take Hopf subalgebra H of H' and a certain order A of H. We see the behavior of Hopfological homology for a tame A-subextension S/R in terms of the surjectivity of trace map and of cyclic modules, which induce Hopf-cyclic homology, for Hopf-Galois extensions with H in terms of relative Hopf modules.