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Abstract
We classify the C 2 × C 2-gradings on M 2(k), k an arbitrary field. If char(k) ≠ 2 our approach relies on the duality between gradings and actions for finite abelian groups, and if k is algebraically closed we find precisely one isomorphism type of grading which is not isomorphic to a grading with all the matrix units being homogeneous elements. If char(k) = 2 we use a computational approach and we find that any C 2 × C 2-grading is induced by a C 2-grading.
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Acknowledgments
I would like to thank the referee for several helpful comments, and to Sorin Dăscălescu for all his support. Research partially supported by Grant 199 of CNCSIS.