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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 2, Pages 196–206
DOI: https://doi.org/10.4213/tmf8645
(Mi tmf8645)
 

This article is cited in 2 scientific papers (total in 2 papers)

Jacobi-type identities in algebras and superalgebras

P. M. Lavrovab, O. V. Radchenkoba, I. V. Tyutinc

a Tomsk State Pedagogical University, Tomsk, Russia
b Tomsk State University, Tomsk, Russia
c Lebedev Physical Institute, RAS, Moscow, Russia
Full-text PDF (415 kB) Citations (2)
References:
Abstract: We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of an arbitrary associative algebra. One is a consequence of the other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an algebra, then the multiplication operation in that algebra is associative. We find a generalization of the obtained results to the super case and give a generalization of the fundamental identity in the case of arbitrary elements. For nondegenerate even symplectic (super)manifolds, we discuss analogues of the fundamental identity.
Keywords: associative algebra, associative superalgebra, Jacobi identity, symplectic supermanifold.
Received: 22.01.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 2, Pages 550–558
DOI: https://doi.org/10.1007/s11232-014-0161-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. M. Lavrov, O. V. Radchenko, I. V. Tyutin, “Jacobi-type identities in algebras and superalgebras”, TMF, 179:2 (2014), 196–206; Theoret. and Math. Phys., 179:2 (2014), 550–558
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8645
  • https://doi.org/10.4213/tmf8645
  • https://www.mathnet.ru/eng/tmf/v179/i2/p196
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:71
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