On abelian unitary involutions of crossed products

Abstract

In the theory of classical linear algebraic groups, of importance are special unitary groups of non-commuted involution crossed products with division. The description of these groups largely depends on the involution type of these products. The class of Abelian involution crossed products is considered and the criterion for their existence is set provided that unitary bases (with respect to these involutions) are present in these products.