The algebra of generic nxn-matrices and its localizations (e.g. the generic division algebra) has attracted much attention among researchers in different areas as PI theory, Brauer theory and algebraic geometry. We construct the corresponding generic objects for an arbitrary finite dimensional G-graded simple algebra where G is a finite group. In particular we construct a generic G-graded Azumaya algebra which represents all forms in the sense of descent theory of a finite dimensional G-graded simple algebra.
Joint work with Y. Karasik.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
