Polynomial identities of M2(G)

Uzi Vishne

doi:10.1081/AGB-120006502

Polynomial identities of M₂(G)

Uzi Vishne

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 M₂(G) (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 PIdeg(M_2,1(G)) ≥ 9 and that M₃(F) has no identities of degree ≤ 8 apart from the consequences of the standard identity S₆.

Original language	English
Pages (from-to)	443-454
Number of pages	12
Journal	Communications in Algebra
Volume	30
Issue number	1
DOIs	https://doi.org/10.1081/AGB-120006502
State	Published - Jan 2002
Externally published	Yes

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AB - We describe an efficient way to use the Sn-module structure in the computation of the multilinear identities of degree n of a given algebra. The method was used to show that M2(G) (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 PIdeg(M2,1(G)) ≥ 9 and that M3(F) has no identities of degree ≤ 8 apart from the consequences of the standard identity S6.

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Polynomial identities of M₂(G)

Abstract

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