4 papers
On a question by Roggenkamp about group algebras
Dylan Johnston, Dmitriy Rumynin
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in…
Disconnected Reductive Groups: Classification and Representations
Dylan Johnston, Diego Martín Duro, Dmitriy Rumynin
In this article, we classify (up to isomorphism) disconnected reductive groups over an algebraically closed field. For the fixed dimension and number of components, our results sho…
Global Representation Ring and Knutson Index
Dylan Johnston, Diego Martín Duro, Dmitriy Rumynin
Global representation rings were discovered by Sarah Witherspoon in 1995 and the Knutson Index was introduced by the second author in 2022. In the present paper we introduce the Kn…
Topological rigidity of -quotients
Dylan Johnston, Dmitriy Rumynin
We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new…