CENTRAL SIMPLE -GRADED ALGEBRAS

ABSTRACT

In this paper we study central simple -graded K-algebras. We obtain structure theorems and define structure elements and invariants for these algebras and characterize their group of graded automorphisms. We define and study their genus and Brauer invariant. In the last part, we present a generalization of the Clifford algebras. These are central simple graded algebras. By translating results of general case, we obtain their properties and their structure. We use these generalized Clifford algebras to compute the obstruction to the solvability of some embedding problems and to construct the solutions when these problems are solvable.

ACKNOWLEDGMENTS

Partially supported by DGES grant PB96-0970-C02-01.