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Specializations of Jordan Superalgebras

Published online by Cambridge University Press:  20 November 2018

Consuelo Martínez  and
Efim Zelmanov
Consuelo Martínez
Affiliation:
Departamento de Matemáticas Universidad de Oviedo C/ Calvo Sotelo, s/n 33007 Oviedo Spain
Efim Zelmanov
Affiliation:
Department of Mathematics Yale University New Haven, CT 06520 USA
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Abstract

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In this paper we study specializations and one-sided bimodules of simple Jordan superalgebras.

Keywords

17C7017C2517C40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 653 - 671
Copyright
Copyright © Canadian Mathematical Society 2002

References

[A] Albert, A., On certain algebra of quantum mechanics. Ann. of Math. (2) 35 (1934), 65–73.Google Scholar
[Be] Bergman, G. M., The diamond lemma for ring theory. Advances in Math. (2) 29 (1978), 178–218.Google Scholar
[Bo] Bokut, L. A., Unsolvability of the word problem and subalgebras of finitely presented Lie algebras. Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 1173–1219.Google Scholar
[C] Cohn, P. M., On homomorphic images of special Jordan algebras. Canad. J. Math. 6 (1954), 253–264.Google Scholar
[CK] Cheng, S. J. and Kac, V., A New N = 6 superconformal algebra. Comm. Math. Phys. 186 (1997), 219–231.Google Scholar
[GLS] Grozman, P., Leites, D. and Shchepochkina, I., Lie superalgebras of string theories. hep-th 9702120.Google Scholar
[J] Jacobson, N., Structure and Representation of Jordan algebras. Amer.Math. Soc., Providence, RI, 1969.Google Scholar
[JNW] Jordan, P., von Newman, J. and Wigner, E., On an algebraic generalization of the quantum mechanical formalism. Ann. of Math. (2) 36 (1934), 29–64.Google Scholar
[Ka1] Kac, V. G., Lie Superalgebras. Advances in Math. 26 (1977), 8–96.Google Scholar
[Ka2] , Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras. Comm. Algebra (13) 5 (1977), 1375–1400.Google Scholar
[KL] Kac, V. G. and van de Leur, J. W., On classification of superconformal algebras. In: Strings ‘88, World Sci. Publishing, Singapore, 1989, 77–106.Google Scholar
[KMZ] Kac, V. G., Martínez, C. and Zelmanov, E., Graded simple Jordan superalgebras of growth one. Mem. Amer.Math. Soc. 150, 2001.Google Scholar
[K1] Kantor, I. L., Connection between Poisson brackets and Jordan and Lie superalgebras. In: Lie theory, differential equations and representation theory (Montreal, 1989), Univ.Montréal, Montréal, QC, 1990, 213–225.Google Scholar
[K2] Kantor, I. L., Jordan and Lie superalgebras defined by Poisson brackets. In: Algebra and Analysis (Tomsk, 1989), Amer.Math. Soc. Transl. Ser. 2 151, Amer. Math. Soc., Providence, RI, 1992, 55–80.Google Scholar
[K-Mc] King, D. and McCrimmon, K., The Kantor construction of Jordan superalgebras. Comm. Algebra (1) 20 (1992), 109–126.Google Scholar
[K-Mc2] King, D. and McCrimmon, K., The Kantor doubling process revisited. Comm. Algebra (1) 23 (1995), 357–372.Google Scholar
[Kp1] Kaplansky, I., Superalgebras. Pacific J. Math. 86 (1980), 93–98.Google Scholar
[Kp2] Kaplansky, I., Graded Jordan Algebras I. Preprint.Google Scholar
[MSZ] Martínez, C., Shestakov, I. and Zelmanov, E., Jordan algebras defined by brackets. J. London Math. Soc. (2) 64 (2001), 357–368.Google Scholar
[MZ] Martínez, C. and Zelmanov, E., Simple finite dimensional Jordan superalgebras of prime characteristic. J. Algebra 236 (2001), 575–629.Google Scholar
[Mc] McCrimmon, K., Speciality and nonspeciality of two Jordan superalgebras. J. Algebra 149 (1992), 326–351.Google Scholar
[MeZ] Medvedev, Y. and Zelmanov, E., Some counterexamples in the theory of Jordan Algebras. In: Nonassociative Algebraic Models (Zaragoza, 1989), Nova Sci. Publ., Commack, NY, 1992, 1–16.Google Scholar
[RZ] Racine, M. and Zelmanov, E., Classification of simple Jordan superalgebras with semisimple even part. J. Algebra, to appear.Google Scholar
[S1] Shestakov, I., Universal enveloping algebras of some Jordan superalgebras. Personal communication.Google Scholar
[Sh1] Shtern, A. S., Representations of an exceptional Jordan superalgebra. Funktsional. Anal. i Prilozhen 21 (1987), 93–94.Google Scholar
[W] Wall, C. T. C., Graded Brauer groups. J. Reine Angew Math. 213 (1964), 187–199.Google Scholar
[Z] Zelmanov, E., On prime Jordan Algebras II. Siberian Math. J. (1) 24 (1983), 89–104.Google Scholar
[ZSSS] Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P. and Shirshov, A. I., Rings that are nearly associative. Academic Press, New York, 1982.Google Scholar