by Vonessen, Nikolaus

Let k be an algebraically closed base field of arbitrary characteristic. In this paper, we study actions of a connected solvable linear algebraic group G on a central simple algebra Q. The main result is the following: Q can be split G-equivariantly by a finite-dimensional splitting field, provided that G acts “algebraically,” i.e., provided that Q contains a G-stable order on which the action is rational. As an application, it is shown that rational torus actions on prime PI-algebras are induced by actions on commutative domains.

DOI: 10.1007/s10468-007-9052-7
Online Date: 5/24/2007
Print publication date: 10/1/2007
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