Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants
HTML articles powered by AMS MathViewer
- by Allan Berele PDF
- Trans. Amer. Math. Soc. 309 (1988), 581-589 Request permission
Abstract:
We prove Razmyslovβs theorem on trace identities for ${M_{k, l}}$ using the invariant theory of $\operatorname {pl} (k, l)$.References
- Itzhak Bars, Supergroups and superalgebras in physics, Phys. D 15 (1985), no.Β 1-2, 42β64. Supersymmetry in physics (Los Alamos, N.M., 1983). MR 784619, DOI 10.1016/0167-2789(85)90147-2
- A. Berele and A. Regev, Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras, Adv. in Math. 64 (1987), no.Β 2, 118β175. MR 884183, DOI 10.1016/0001-8708(87)90007-7 A. R. Kemer, Varieties and ${Z_2}$-graded algebras, Math. USSR Izv. 25 (1985), 359-374.
- D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc. 181 (1973), 429β438. MR 325658, DOI 10.1090/S0002-9947-1973-0325658-5
- C. Procesi, The invariant theory of $n\times n$ matrices, Advances in Math. 19 (1976), no.Β 3, 306β381. MR 419491, DOI 10.1016/0001-8708(76)90027-X Yu. P. Razmyslov, Trace identities of full matrix algebra over a field of characteristic zero, Algebra i Logika 12 (1973), 47-63.
- Yu. P. Razmyslov, Trace identities and central polynomials in matrix superalgebras $M_{n,k}$, Mat. Sb. (N.S.) 128(170) (1985), no.Β 2, 194β215, 287 (Russian). MR 809485
- Amitai Regev, Sign trace identities, Linear and Multilinear Algebra 21 (1987), no.Β 1, 1β28. MR 897942, DOI 10.1080/03081088708817776
- T. Y. Lam, The algebraic theory of quadratic forms, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1973. MR 0396410
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 581-589
- MSC: Primary 17B70; Secondary 15A24, 15A69, 22E60
- DOI: https://doi.org/10.1090/S0002-9947-1988-0938917-0
- MathSciNet review: 938917