The Grassmann algebra, E, generated by an infinite dimensional vector space, L, and its Z2-graded polynomial identities play an important role in Kemer’s structure theory on varieties of associative algebras with polynomial identities. In this paper we study the Z2-graded polynomial identities of E with respect to any fixed Z2-grading such that L is an homogeneous sub-space. We found explicit generators for the ideal, T_2(E), of graded polynomial identities of E and we determine its graded-cocharacter and graded-codimension sequences.

On Z_2-graded polynomial identities of the Grassmann Algebra

DI VINCENZO, Onofrio Mario;
2009

Abstract

The Grassmann algebra, E, generated by an infinite dimensional vector space, L, and its Z2-graded polynomial identities play an important role in Kemer’s structure theory on varieties of associative algebras with polynomial identities. In this paper we study the Z2-graded polynomial identities of E with respect to any fixed Z2-grading such that L is an homogeneous sub-space. We found explicit generators for the ideal, T_2(E), of graded polynomial identities of E and we determine its graded-cocharacter and graded-codimension sequences.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/2610
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