Central Simple Z_d-graded Algebras
by
Cemal Koç
Dogus University, Istanbul, Turkey

In [W], C.T.C. Wall established the theory of central simple Z₂-graded algebras and recently in [K-Ku] C.Koç and Y. Kurtulmaz investigated the structure of  Bbb Z_d-graded algebras and established decomposition theorems for central simple Z_p-graded algebras when p is a prime number. In this paper we extend these decomposition theorems to Z_d-graded algebras for an arbitrary integer d and as an application we give the complete structure theory of generalized Clifford algebras. We also provide a short proof to the decomposition results given by T.L. Smith in [S].

References

[K-Ku] Koç, C., Kurtulmaz, Y.: Structure of Central Simple Graded Algebras, (To appear)

[L] Lam, T.Y.: The Algebraic Theory of Quadratic Forms, W.A. Benjamin, Inc., 1973

[S] Smith, T.L., Decomposition of Generalized Clifford Algebras, Quart. J. Math. Oxford (2), 42 (1991), 105-112.

[W] Wall, C.T., Graded Brauer Groups, J. reine angew. Maths., 213 (1964), 187-199

Date received: July 24, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafe-42.