Topological Hopf algebras and their Hopf-cyclic cohomology
MetadataShow full item record
CitationRangipour, B. & Sütlü, S. S. (2019). Topological hopf algebras and their hopf-cyclic cohomology. Communications in Algebra, 47(4), 1490-1515. doi:10.1080/00927872.2018.1508581
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.