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Group gradings of M2(K)

Published online by Cambridge University Press:  17 April 2009

R. Khazal ,
Crina Boboc  and
S. Dăscălescu
R. Khazal
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, Safat 13060, Kuwait, e-mail: [email protected]
Crina Boboc
Affiliation:
University of Bucharest, Faculty of Physics, Măgurele, Bucharest, Romania, e-mail: [email protected]
S. Dăscălescu
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, Safat 13060, Kuwait, e-mail: [email protected]
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Abstract

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We describe all group gradings of the matrix algebra M2(k), where k is an arbitrary field. We prove that any such grading reduces to a grading of type C2, a grading of type C2 × C2, or to a good grading. We give new simple proofs for the description of C2-gradings and C2 × C2-gradings on M2(K).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 285 - 293
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Bahturin, Yu. A., Sehgal, S.K. and Zaicev, M.V., ‘Group gradings on associative algebras’, J. Algebra 241 (2001), 677–698.CrossRefGoogle Scholar
[2]Boboc, C., ‘Superalgebra structures on M 2(k) in characteristic 2’, Comm. Algebra 30 (2002), 255–260.CrossRefGoogle Scholar
[3]Boboc, C., ‘Gradings of M 2(k) by the Klein group’, Comm. Algebra 31 (2003), 2311–2326.CrossRefGoogle Scholar
[4]Boboc, C. and Dăscălescu, S., ‘Gradings of matrix algebras by cyclic groups’, Comm. Algebra 29 (2001), 5013–5021.CrossRefGoogle Scholar
[5]Caenepeel, S., Dăscălescu, S. and Năstăsescu, C., ‘On gradings of matrix algebras and descent theory’, Comm. Algebra 30 (2002), 5901–5920.CrossRefGoogle Scholar
[6]Dăscălescu, S., Ion, B., Năstăsescu, C. and Montes, J. Rios, ‘Group gradings on full matrix rings’, J. Algebra 220 (1999), 709–728.CrossRefGoogle Scholar
[7]Green, E.L., ‘Graphs with relations, coverings and group-graded algebras’, Trans. Amer. Math. Soc. 279 (1983), 297–310.CrossRefGoogle Scholar
[8]Kelarev, A.V., ‘Applications of epigroups to graded ring theory’, Semigroup Forum 50 (1995), 327–350.CrossRefGoogle Scholar
[9]Năstăsescu, C. and Van Oystaeyen, F., Graded ring theory (North Holland, Amsterdam, New York, 1982).Google Scholar
[10]Zaicev, M.V. and Segal, S.K., ‘Finite gradings on simple artinian rings’, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 3 (2001), 21–24.Google Scholar