Seminário Especial de Álgebras de Hopf e Categorias Monoidais
Reductions of Piecewise-Trivial Principal Comodule Algebras
Prof. Dr. Piotr M. Hajac (IMPAN-Polônia)
Abstract: Let G’ be a closed subgroup of a topological group G. A principal G-bundle X is reducible to a locally trivial principal G’-bundle if and only if there exists a local trivialisation of X such that all transition functions take values in G’. The goal of this talk is to unravel a noncommutative-geometric counterpart of this theorem. To this end, we employ the concept of a piecewise-trivial principal comodule algebra as a generalization of a piecewise-trivial compact principal bundle and a replacement of a locally trivial principal bundle. To illustrate our theorem, first we define a new noncommutative deformation of a nontrivial but reducible U(1)-principal bundle that yields a piecewise-trivial principal comodule algebra. Then we instantiate the theorem by explaining how the thus obtained piecewise-trivial principal comodule algebra is reducible much as its classical counterpart is reducible. To end with, using K-theory, we show that the principal comodule algebra is not cleft. (Based on joint work with Jan Rudnik and Bartosz Zieliński.)
Data: Segunda-feira, 20 de Novembro de 2023, 16:00h
Local: Auditório Airton Silva, Departamento de Matemática – MTM /CFM