Every group is automorphism group of a simple algebra

Abstract: Popov raised the question whether each finite group is the automorphism group of a finite dimensional simple algebra. He and Gordeev provided an affirmative answer for sufficiently large enough fields, not only for finite groups, but also for algebraic groups. We will show that for each field F and each (finite) group G there are infinitely many (finite) dimensional simple algebras with G as automorphism group. If F has at least 4 elements the algebras can be commutative as well as non-commutative.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar