Graded Central Polynomials forT-Prime Algebras

Le résumé fourni par la source

Let K be a field, char K = 0, and let E = E 0⊕ E 1 be the Grassmann algebra of infinite dimension over K, equipped with its natural ℤ2-grading. If G is a finite abelian group and R = ⨁ g∈G R (g) is a G-graded K-algebra, then the algebra R⊗ E can be G × ℤ2-graded by setting (R⊗ E)(g, i) = R (g) ⊗ E i . In this article we describe the graded central polynomials for the T-prime algebras M n (E)≅ M n (K)⊗ E. As a corollary we obtain the graded central polynomials for the algebras M a, b (E)⊗ E. As an application, we determine the ℤ2-graded identities and central polynomials for E⊗ E.

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