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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.

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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