A minimal basis of identities for a second-order matrix algebra over a field of characteristic 0. (English. Russian original) Zbl 0496.16017
Algebra Logic 20, 188-194 (1982); translation from Algebra Logika 20, 282-290 (1981).
MSC:
| 16Rxx | Rings with polynomial identity |
| 17B99 | Lie algebras and Lie superalgebras |
| 16S50 | Endomorphism rings; matrix rings |
Keywords:
algebra of 2x2 matrices; polynomial identities; basis for T-ideal; multilinear polynomials; free algebra; irreducible modulesReferences:
| [1] | Yu. P. Razmyslov, ”Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero,” Algebra Logika,12, No. 1, 83–113 (1973). |
| [2] | V. T. Filippov, ”Varieties of Mal’tsev algebras,” Algebra Logika,20, No. 3, 300–314 (1981). |
| [3] | H. Weyl, The Classical Groups. Their Invariants and Representations, Princeton Univ. Press (1946). · Zbl 1024.20502 |
| [4] | V. S. Drenski, ”Representations of the symmetric group and varieties of linear algebras,” Mat. Sb.,115, No. 1, 98–115 (1981). · Zbl 0465.17007 |
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