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Some constructions for Jordan superalgebras with associative even part


Authors: V. N. Zhelyabin and A. S. Zakharov
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 28 (2016), nomer 2.
Journal: St. Petersburg Math. J. 28 (2017), 197-208
MSC (2010): Primary 16W10; Secondary 17C50
DOI: https://doi.org/10.1090/spmj/1446
Published electronically: February 15, 2017
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Abstract: A construction is presented that enables one to build Jordan superalgebras by using Jordan superalgebras with associative even part. This is a generalization of a known construction of the addition of an odd variable in the case of superalgebras of Jordan brackets. Previously, this construction was described for simple special Jordan algebras with associative even part.


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Additional Information

V. N. Zhelyabin
Affiliation: Novosibirsk State University, ul. Pirogova 2, 630090 Novosibirsk, Russia
Email: vicnic@math.nsc.ru

A. S. Zakharov
Affiliation: Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Academician Koptyug pr. 4, 630090 Novosibirsk, Russia
Email: antzakh@gmail.com

DOI: https://doi.org/10.1090/spmj/1446
Keywords: Jordan superalgebra, superalgebra of vector type, Poisson bracket, differential algebra, projective module
Received by editor(s): April 1, 2015
Published electronically: February 15, 2017
Additional Notes: Supported by RSF (project no. 14-21-00065)
Article copyright: © Copyright 2017 American Mathematical Society