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JORDAN SUPERALGEBRAS DEFINED BY BRACKETS

Published online by Cambridge University Press:  30 October 2001

CONSUELO MARTÍNEZ ,
IVAN SHESTAKOV  and
EFIM ZELMANOV
CONSUELO MARTÍNEZ
Affiliation:
Departamento de Matemáticas, Universidad de Oviedo, C/Calvo Sotelo, s/n 33007, Oviedo, Spain; chelo@pinon.ccu.uniovi.es
IVAN SHESTAKOV
Affiliation:
Instituto de Mathemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 – CEP 05315-970, São Paulo, Brazil Sobolev Institute of Mathematics, Novosibirsk 630090, Russia; shestak@ime.usp.br
EFIM ZELMANOV
Affiliation:
Department of Mathematics, Yale University, New Haven, CT 06520, USA KIAS, Seoul 130-012, South Korea; zelmanov@math.yale.edu
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Abstract

Jordan superalgebras defined by brackets on associative commutative superalgebras are studied. It is proved that any such superalgebra is imbedded into a superalgebra defined by Poisson brackets. In particular, all Jordan superalgebras of brackets are i-special. The speciality of these superalgebras is also examined, and it is proved, in particular, that the Cheng–Kac superalgebra is special.

Information

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 357 - 368
Copyright
The London Mathematical Society 2001

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