Jordan bimodules over the superalgebras $P(n)$ and $Q(n)$
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- by Consuelo Martínez, Ivan Shestakov and Efim Zelmanov PDF
- Trans. Amer. Math. Soc. 362 (2010), 2037-2051 Request permission
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 $Q(2)$.References
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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
- MR Author ID: 289548
- 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
- MR Author ID: 189654
- Email: ezelmano@maths.ucsd.edu
- 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 - © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 362 (2010), 2037-2051
- MSC (2000): Primary 17C70; Secondary 17C55, 17B10, 17B60
- DOI: https://doi.org/10.1090/S0002-9947-09-04997-6
- MathSciNet review: 2574886