POLYNOMIAL IDENTITIES OF

ABSTRACT

We describe an efficient way to use the S_n -module structure in the computation of the multilinear identities of degree n of a given algebra. The method was used to show that (where G is the Grassmann algebra) has identities of degree 8, but of no smaller degree. Explicit identities of degree 8 are given. It was also checked that and that has no identities of degree ≤ 8 apart from the consequences of the standard identity .

Acknowledgments