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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On $ \delta$-superderivations of simple superalgebras of Jordan brackets


Authors: V. N. Zhelyabin and I. B. Kaygorodov
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 23 (2011), nomer 4.
Journal: St. Petersburg Math. J. 23 (2012), 665-677
MSC (2010): Primary 17A70
Published electronically: April 13, 2012
MathSciNet review: 2893521
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Abstract: A complete description of $ \delta $-derivations and $ \delta $-superderivations is given for simple unital superalgebras of Jordan brackets over a field of characteristic different from 2 and for simple unital finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic $ p \neq 2$. As a consequence, a criterion for simple unital superalgebras of Jordan brackets to be special is obtained.


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Additional Information

V. N. Zhelyabin
Affiliation: Sobolev Institute of Mathematics, Sibir Branch of Russian Academy of Sciences, Academician Koptyug Avenue 4, Novosibirsk 630090, Russia
Email: vicnic@math.nsc.ru

I. B. Kaygorodov
Affiliation: Novosibirsk State University, Pirogov Street 2, Novosibirsk 630090, Russia
Email: kib@math.nsc.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01213-6
PII: S 1061-0022(2012)01213-6
Keywords: $𝛿$-superdifferentiation, $𝛿$-differentiation, Jordan superalgebra, Cantor double
Received by editor(s): January 7, 2010
Published electronically: April 13, 2012
Additional Notes: Supported by the Analytic Departmental Special Program “Development of the Scientific potential of Higher School” of the Federal Educational Agency (project 2.1.1.419), by RFBR grants nos. 09-01-00157-A, 11-01-00938-A, by RF President Grant council for support of young scientists and leading scientific schools (project NSh-3669.2010.1), by Special Federal program “Scientific and Pedagogical staff of innovative Russia” for 2009–2013 (state contracts nos. 02.740.11.0429, 02.740.11.5191, 14.740.11.0346), by integrational project of SD RAS no. 97, and by Lavrent’ev grant for young scientists’ collectives by SD RAS, Decision of the Presidium of SD RAS no. 43 of 04.02.2010
Article copyright: © Copyright 2012 American Mathematical Society