On \(\mathbb Z_2\)-graded polynomial identities of the Grassmann algebra. (English) Zbl 1225.16009
Summary: Let \(F\) be a field of characteristic zero and let \(E\) be the Grassmann algebra of an infinite dimensional \(F\)-vector space \(L\). In this paper we study the \(\mathbb Z_2\)-graded polynomial identities of \(E\) with respect to any fixed \(\mathbb Z_2\)-grading such that \(L\) is a homogeneous subspace. We find explicit generators for the ideal, \(T_2(E)\), of graded polynomial identities of \(E\) and we determine its cocharacter and codimension sequences.
MSC:
| 16R50 | Other kinds of identities (generalized polynomial, rational, involution) |
| 16R10 | \(T\)-ideals, identities, varieties of associative rings and algebras |
| 15A75 | Exterior algebra, Grassmann algebras |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16W55 | “Super” (or “skew”) structure |
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