P.I. envelopes of classical simple Lie superalgebras

Musson, Ian

doi:10.1090/S0002-9939-02-06481-X

P.I. envelopes of classical simple Lie superalgebras
HTML articles powered by AMS MathViewer

by Ian M. Musson

Proc. Amer. Math. Soc. 130 (2002), 3185-3191

DOI: https://doi.org/10.1090/S0002-9939-02-06481-X

Published electronically: March 25, 2002

PDF | Request permission

Abstract:

Let $\mathfrak {g}$ be a classical simple Lie superalgebra. We describe the prime ideals $P$ in the enveloping algebra $U(\mathfrak {g})$ such that $U(\mathfrak {g})/P$ satisfies a polynomial identity. If the factor algebra $U(\mathfrak {g})/P$ is not artinian, then it is an order in a matrix algebra over $K(z)$.

References

Yuri Bahturin and Susan Montgomery, PI-envelopes of Lie superalgebras, Proc. Amer. Math. Soc. 127 (1999), no. 10, 2829–2839. MR 1600092, DOI 10.1090/S0002-9939-99-04825-X
Walter Borho, Peter Gabriel, and Rudolf Rentschler, Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume), Lecture Notes in Mathematics, Vol. 357, Springer-Verlag, Berlin-New York, 1973 (German). MR 0376790
K. A. Brown and S. P. Smith, Bimodules over a solvable algebraic Lie algebra, Quart. J. Math. Oxford Ser. (2) 36 (1985), no. 142, 129–139. MR 790475, DOI 10.1093/qmath/36.2.129
A. V. Jategaonkar, Localization in Noetherian rings, London Mathematical Society Lecture Note Series, vol. 98, Cambridge University Press, Cambridge, 1986. MR 839644, DOI 10.1017/CBO9780511661938
V. G. Kac, Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. MR 486011, DOI 10.1016/0001-8708(77)90017-2
V. Kac, Representations of classical Lie superalgebras, Differential geometrical methods in mathematical physics, II (Proc. Conf., Univ. Bonn, Bonn, 1977) Lecture Notes in Math., vol. 676, Springer, Berlin, 1978, pp. 597–626. MR 519631
Edward Letzter, Primitive ideals in finite extensions of Noetherian rings, J. London Math. Soc. (2) 39 (1989), no. 3, 427–435. MR 1002455, DOI 10.1112/jlms/s2-39.3.427
Edward S. Letzter, Finite correspondence of spectra in Noetherian ring extensions, Proc. Amer. Math. Soc. 116 (1992), no. 3, 645–652. MR 1098402, DOI 10.1090/S0002-9939-1992-1098402-1
Edward S. Letzter, A bijection of primitive spectra for classical Lie superalgebras of type I, J. London Math. Soc. (2) 53 (1996), no. 1, 39–49. MR 1362685, DOI 10.1112/jlms/53.1.39
S. Minakshi Sundaram, On non-linear partial differential equations of the hyperbolic type, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 495–503. MR 0000089