Representation theory of Jordan superalgebras I

Martínez, Consuelo; Zelmanov, Efim

doi:10.1090/S0002-9947-09-04883-1

Representation theory of Jordan superalgebras I
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by Consuelo Martínez and Efim Zelmanov PDF

Trans. Amer. Math. Soc. 362 (2010), 815-846 Request permission

Abstract:

We complete the classification of irreducible bimodules over simple finite dimensional Jordan superalgebras.

References

Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
V. G. Kac, Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5 (1977), no. 13, 1375–1400. MR 498755, DOI 10.1080/00927877708822224
I. L. Kantor, Jordan and Lie superalgebras determined by a Poisson algebra, Algebra and analysis (Tomsk, 1989) Amer. Math. Soc. Transl. Ser. 2, vol. 151, Amer. Math. Soc., Providence, RI, 1992, pp. 55–80. MR 1191172, DOI 10.1090/trans2/151/03
Irving Kaplansky, Superalgebras, Pacific J. Math. 86 (1980), no. 1, 93–98. MR 586871
I. Kaplansky, Graded Jordan Algebras I, Preprint.
Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721
C. Martínez and I. Shestakov, Unital irreducible bimodules over $M_{1+1}$, Preprint.
Consuelo Martínez, Ivan Shestakov, and Efim Zelmanov, Jordan superalgebras defined by brackets, J. London Math. Soc. (2) 64 (2001), no. 2, 357–368. MR 1853456, DOI 10.1112/S0024610701002290
C. Martínez, I. Shestakov and E. Zelmanov, Jordan bimodules over the superalgebras $P(n)$ and $Q(n)$, Submitted
Consuelo Martínez and Efim I. Zelmanov, Lie superalgebras graded by $P(n)$ and $Q(n)$, Proc. Natl. Acad. Sci. USA 100 (2003), no. 14, 8130–8137. MR 1989345, DOI 10.1073/pnas.0932706100
Consuelo Martínez and Efim Zelmanov, Specializations of Jordan superalgebras, Canad. Math. Bull. 45 (2002), no. 4, 653–671. Dedicated to Robert V. Moody. MR 1941232, DOI 10.4153/CMB-2002-059-8
Consuelo Martínez and Efim Zelmanov, Unital bimodules over the simple Jordan superalgebra $D(t)$, Trans. Amer. Math. Soc. 358 (2006), no. 8, 3637–3649. MR 2218992, DOI 10.1090/S0002-9947-05-03821-3
C. Martínez and E. Zelmanov, Representation theory of Jordan superalgebras II, Preprint.
Yu. A. Medvedev and E. I. Zel′manov, Some counterexamples in the theory of Jordan algebras, Nonassociative algebraic models (Zaragoza, 1989) Nova Sci. Publ., Commack, NY, 1992, pp. 1–16. MR 1189608
N. A. Pisarenko, The structure of alternative superbimodules, Algebra i Logika 33 (1994), no. 6, 689–707, 717 (Russian, with Russian summary); English transl., Algebra and Logic 33 (1994), no. 6, 386–397 (1995). MR 1347266, DOI 10.1007/BF00756352
A. S. Shtern, Representations of an exceptional Jordan superalgebra, Funktsional. Anal. i Prilozhen. 21 (1987), no. 3, 93–94 (Russian). MR 911787
M. N. Trushina, Irreducible representations of a certain Jordan superalgebra, J. Algebra Appl. 4 (2005), no. 1, 1–14. MR 2130461, DOI 10.1142/S0219498805001010
C. T. C. Wall, Graded Brauer groups, J. Reine Angew. Math. 213 (1963/64), 187–199. MR 167498, DOI 10.1515/crll.1964.213.187
K. A. Zhevlakov, A. M. Slin′ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, vol. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. Translated from the Russian by Harry F. Smith. MR 668355