2023/12/20 by Jacopo Zanchettin, Zanchettin, Jacopo · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2312.12927
In this article, we study the Chern-Weil theory for Hopf-Galois extensions originally introduced by Hajac and Maszczyk in the context of coalgebra extensions. We show that the cyclic homology Chern-Weil homomorphism defines natural transformations between Hopf-Galois extensions with a strong connection (principal comodule algebras) and cyclic homology, thereby generalizing the concept of characteristic classes to the noncommutative setting. In the second part, we study the effect of 2-cocycle deformations of Hopf-Galois extensions on the aforementioned homomorphism. We consider the 2-cocycle coming from the structure Hopf algebra of the extension, an external symmetry, and finally the combined case.