2015/04/26 by Bahram Rangipour, Rangipour, Bahram, Serkan Sütlü +1
Mathematics · #16S40 #19D55 #57T05 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:16S40 #msc:19D55 #msc:57T05
paper · pdf · doi:10.48550/arxiv.1504.06834
Further revisions
arxiv created 2018/07/26 · arxiv updated 2018/07/30
A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of coefficients (AYD modules) over a topological Lie algebra and those over its universal enveloping (Hopf) algebra are isomorphic. For topological Hopf algebras, the category of coefficients is identified with the representation category of a topological algebra called the anti-Drinfeld double. Finally, a topological van Est type isomorphism is detailed, connecting the Hopf-cyclic cohomology to the relative Lie algebra cohomology with respect to a maximal compact subalgebra.