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|Type:||Artigo de periódico|
|Title:||Central polynomials for Z(2)-graded algebras and for algebras with involution|
|Abstract:||We describe the Z(2)-graded central polynomials for the matrix algebra of order two, M-2(K), and for the algebras M-1.1 (E) and E circle times E over an infinite field K, char K not equal 2. Here E is the infinite-dimensional Grassmann algebra, and M-1.1 (E) stands for the algebra of the 2 x 2 matrices whose entries on the diagonal belong to E-0, the centre of E, and the off-diagonal entries lie in E-1, the anticommutative part of E. It turns out that in characteristic 0 the graded central polynomials for M-1.1 (E) and E circle times E are the same (it is well known that these two algebras satisfy the same polynomial identities when char K = 0). On the contrary, this is not the case in characteristic p > 2. We describe systems of generators for the Z(2)-graded central polynomials for all these algebras. Finally we give a generating set of the central polynomials with involution for M-2(K). We consider the transpose and the symplectic involutions. (c) 2006 Elsevier B.V. All rights reserved.|
|Editor:||Elsevier Science Bv|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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