Drensky, Vesselin; Kasparian, Azniv Polynomial identities of eighth degree for \(3\times 3\) matrices. (English) Zbl 0736.16012 God. Sofij. Univ., Fak. Mat. Mekh. 77(1983), No. 1, 175-195 (1988). The authors prove that all identities of eighth degree for the \(3\times 3\) matrix algebra \(M_ 3(K)\) over a field \(K\) of characteristic zero are consequences of the standard identity \(S_ 6(x_ 1,\dots,x_ 6)\), calculate the \(\text{Sym}(8)\)-character of the multilinear identities in 8 variables, obtain all central polynomials of degree 8 for \(M_ 3(K)\) and study identities of \(sl_ 3(K)\). All results are obtained by the methods of the representation theory of symmetric and general linear groups. Reviewer: Yu.N.Mal’tsev (Barnaul) Cited in 1 ReviewCited in 12 Documents MSC: 16R10 \(T\)-ideals, identities, varieties of associative rings and algebras Keywords:\(3\times 3\) matrix algebra; standard identity; multilinear identities; central polynomials × Cite Format Result Cite Review PDF