Domokos, Mátyás and Drensky, Vesselin (2020) Cocharacters for the weak polynomial identities of the Lie algebra of 3 × 3 skewsymmetric matrices. ADVANCES IN MATHEMATICS, 374. ISSN 00018708

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Abstract
Let so3(K) be the Lie algebra of 3×3 skewsymmetric matrices over a field K of characteristic 0. The ideal I(M3(K),so3(K)) of the weak polynomial identities of the pair (M3(K),so3(K)) consists of the elements f(x1,…,xn) of the free associative algebra K〈X〉 with the property that f(a1,…,an)=0 in the algebra M3(K) of all 3×3 matrices for all a1,…,an∈so3(K). The generators of I(M3(K),so3(K)) were found by Razmyslov in the 1980s. In this paper the cocharacter sequence of I(M3(K),so3(K)) is computed. In other words, the GLp(K)module structure of the algebra generated by p generic skewsymmetric matrices is determined. Moreover, the same is done for the closely related algebra of SO3(K)equivariant polynomial maps from the space of ptuples of 3×3 skewsymmetric matrices into M3(K) (endowed with the conjugation action). In the special case p=3 the latter algebra is a module over a 6variable polynomial subring in the algebra of SO3(K)invariants of triples of 3×3 skewsymmetric matrices, and a free resolution of this module is found. The proofs involve methods and results of classical invariant theory, representation theory of the general linear group and explicit computations with matrices. © 2020 The Author(s)
Item Type:  Article 

Uncontrolled Keywords:  classical invariant theory; Skewsymmetric matrices; Weak polynomial identities; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  29 Aug 2020 07:30 
Last Modified:  21 Apr 2023 10:43 
URI:  http://real.mtak.hu/id/eprint/112597 
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