A remark on automorphisms of tensor spaces

Abstract

A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can occur as the automorphism groups of such tensor spaces. Using this, we show that a tensor space can behave somewhat pathologically as a representation of its automorphism group.

5 pages