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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Jordan bimodules over the superalgebras $ P(n)$ and $ Q(n)$


Authors: Consuelo Martínez, Ivan Shestakov and Efim Zelmanov
Journal: Trans. Amer. Math. Soc. 362 (2010), 2037-2051
MSC (2000): Primary 17C70; Secondary 17C55, 17B10, 17B60
Published electronically: November 13, 2009
MathSciNet review: 2574886
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Abstract: We extend the Jacobson's Coordinatization theorem to Jordan superalgebras. Using it we classify Jordan bimodules over superalgebras of types $ Q(n)$ and $ JP(n)$, $ n \geq 3$. Then we use the Tits-Kantor-Koecher construction and representation theory of Lie superalgebras to treat the remaining case $ Q(2)$.


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Additional Information

Consuelo Martínez
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo, s/n, 33007 Oviedo, Spain
Email: cmartinez@uniovi.es

Ivan Shestakov
Affiliation: Instituto de Matemática e Estadística, Universidade de São Paulo, Caixa Postal 66281,CEP 05315-970, São Paulo, Brasil
Email: shestak@ime.usp.br

Efim Zelmanov
Affiliation: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 – and – Korea Institute for Advanced Study, Seoul 130-012, Korea
Email: ezelmano@maths.ucsd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04997-6
PII: S 0002-9947(09)04997-6
Keywords: Jordan superalgebra, Jordan bimodule
Received by editor(s): February 27, 2008
Published electronically: November 13, 2009
Additional Notes: The first author was partially supported by MTM 2007-067884-C04-01 and FICYT IB-08-147. The author also thanks KIAS for their hospitality.
The second author was partially supported by the CNPq grant 304991/2006-6 and the FAPESP grants 05/60337-2, 05/60142-7. The author also thanks Oviedo University for their hospitality.
The third author was partially supported by the NSF
Article copyright: © Copyright 2009 American Mathematical Society