Structure theory of central simple $Bbb{Z}_d$-graded algebras

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

This paper investigates the structure theory of $Bbb{Z}$d- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of $Bbb{Z}$d-central simple graded algebras.

PDF

___

[1] Beattie, M., Caenepeel, S.: The Brauer-Long group of $Bbb{Z}/p^{t}Bbb{Z}$-dimodule algebras. Journal of Pure and Applied Algebra 60, 219–236 (1989).
[2] Beattie, M., Caenepeel, S.: A cohomological approach to the Brauer-Long group and the groups of Galois extensions and strongly graded rings. Trans. Amer. Math. Soc. 324, 747–775 (1991).
[3] Childs, L.N., Garfinkel, G., Orzech, M.: The Brauer Group of graded Azumaya algebras. Transactions of the American Mathematical Society 175, 299–326 (1973).
[4] Van Oystaeyen, F., Zhang, Y.: Brauer groups of actions. In: Rings, Hopf Algebras, and Brauer Groups, (Eds.: S. Caenepeel and A. Verschoren) 299–326, Marcel Dekker (1998).
[5] Jacobson, N.: Lectures in Abstract Algebra, Volume II., D. Van Nostrand Company, Inc. (1953).
[6] Ko¸c, C.: Clifford algebras of d-Forms, Turkish Journal of Math., 19, 301–311 (1995).
[7] Knus, M.A.: Algebras graded by a group. Lecture Notes in Math. 92, Springer Verlag, Berlin, 117–133 (1969).
[8] Lam, T.Y.: The algebraic kheory of Quadratic Forms. W.A. Benjamin, Inc., (1973).
[9] Vela, M.: Central simple $Bbb{Z}/nBbb{Z}$-graded algebras. Communications in Algebra 30, 1995–2021 (2002).
[10] Wall, C.T.: Graded Brauer groups J. Reine Angew. Maths. 213, 187-199 (1964).
[11] Warden, V. der: Modern Algebra. Ungar (1966).