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New generalized simple Lie algebras of Cartan type over a field with characteristic 0. (English) Zbl 0955.17019

The author constructs four new series of generalized simple Lie algebras of Cartan type. His results are further generalizations of those in J. M. Osborn [J. Algebra 185, No. 3, 820–835 (1996; Zbl 0874.17024)].

MSC:

17B20 Simple, semisimple, reductive (super)algebras

Citations:

Zbl 0874.17024

References:

[1] Block, R.: On torsion-free abelian groups and Lie algebras. Proc. amer. Math. soc. 9, 613-620 (1958) · Zbl 0087.26302
[2] Doković, D.; Zhao, K.: Generalized Cartan type W Lie algebras in characteristic 0. J. algebra 195, 170-210 (1997) · Zbl 0886.17019
[3] Kac, V. G.: A description of filtered Lie algebras whose associated graded Lie algebras are of Cartan types. Math. USSR-izvestija 8, 801-835 (1974) · Zbl 0317.17002
[4] Kac, V. G.: Lie superalgebras. Adv. math. 26, 8-96 (1977) · Zbl 0366.17012
[5] Kac, V. G.: Vertex algebras for beginners. University lectures series 10 (1996) · Zbl 0861.17017
[6] Kac, V. G.: Superconformal algebras and transitive group actions on quadrics. Comm. math. Phys. 186, 233-252 (1997) · Zbl 0886.17021
[7] Kac, V. G.; Leur, J. W.: On classification of superconformal algebras. String 88, 77-106 (1989) · Zbl 0938.17500
[8] Kac, V. G.; Todorov, I. T.: Superconformal current algebras and their unitary representations. Comm. math. Phys. 102, 337-347 (1985) · Zbl 0599.17011
[9] Kawamoto, N.: Generalizations of Witt algebras over a field of characteristic zero. Hiroshima math. J. 16, 417-462 (1986) · Zbl 0607.17008
[10] Osborn, J. Marshall: Infinite dimensional Novikov algebras of characteristic 0. J. algebra 167, 146-167 (1994) · Zbl 0814.17002
[11] Osborn, J. Marshall: New simple infinite-dimensional Lie algebras of characteristic 0. J. algebra 185, 820-835 (1996) · Zbl 0874.17024
[12] Passman, D. P.: Simple Lie algebras of Witt type. J. algebra 206, 682-692 (1998) · Zbl 0907.17006
[13] Strade, H.; Farnsteiner, R.: Modular Lie algebras and their representations. (1988) · Zbl 0648.17003
[14] Xu, X.: On simple Novikov algebras and their irreducible modules. J. algebra 185, 905-934 (1996) · Zbl 0863.17003
[15] X. Xu, Variational calculus of supervariables and related algebraic structures, J. Algebra, in press. · Zbl 1012.37048
[16] Xu, X.: Novikov-Poisson algebras. J. algebra 190, 253-279 (1997) · Zbl 0872.17030
[17] X. Xu, Quadratic conformal superalgebras, submitted for publication.
[18] Xu, X.: Introduction to vertex operator superalgebras and their modules. (1998) · Zbl 0929.17030
[19] X. Xu, Generalizations of Block algebras, Manuscripta Mathematica, in press. · Zbl 1027.17007
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