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|Type:||Artigo de periódico|
|Title:||Central Polynomials For Z2-graded Algebras And For Algebras With Involution|
|Author:||Pereira Brandao Jr. A.|
|Abstract:||We describe the Z2-graded central polynomials for the matrix algebra of order two, M2 (K), and for the algebras M1, 1 (E) and E ⊗ E over an infinite field K, char K ≠ 2. Here E is the infinite-dimensional Grassmann algebra, and M1, 1 (E) stands for the algebra of the 2 × 2 matrices whose entries on the diagonal belong to E0, the centre of E, and the off-diagonal entries lie in E1, the anticommutative part of E. It turns out that in characteristic 0 the graded central polynomials for M1, 1 (E) and E ⊗ 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 Z2-graded central polynomials for all these algebras. Finally we give a generating set of the central polynomials with involution for M2 (K). We consider the transpose and the symplectic involutions. © 2006 Elsevier Ltd. All rights reserved.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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