Skip to main content

Fields of Definition for Representations of Associative Algebras

Citations of this article
Mendeley users who have this article in their library.
Get full text
This PDF is freely available from an open access repository. It may not have been peer-reviewed.


We examine situations, where representations of a finite-dimensional F-algebra A defined over a separable extension field K/F, have a unique minimal field of definition. Here the base field F is assumed to be a field of dimension a-1. In particular, F could be a finite field or k(t) or k((t)), where k is algebraically closed. We show that a unique minimal field of definition exists if (a) K/F is an algebraic extension or (b) A is of finite representation type. Moreover, in these situations the minimal field of definition is a finite extension of F. This is not the case if A is of infinite representation type or F fails to be of dimension a-1. As a consequence, we compute the essential dimension of the functor of representations of a finite group, generalizing a theorem of Karpenko, Pevtsova and the second author.




Benson, D., & Reichstein, Z. (2019). Fields of Definition for Representations of Associative Algebras. Proceedings of the Edinburgh Mathematical Society, 62(1), 291–304.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free