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TMF, 1993, Volume 94, Number 2, Pages 213–231 (Mi tmf1418)  

This article is cited in 6 scientific papers (total in 6 papers)

Paragrassmann differential calculus

A. T. Filippov, A. P. Isaev, A. B. Kurdikov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: This paper significantly extends and generalizes the paragrassmann calculus of our previous paper [1]. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable, nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of $(p+1)\times (p+1)$ complex matrices. If $(p+1)$ is a prime integer, the algebra is nondegenerate and so unique. We then give a general construction of many-variable diffeentiation algebras. Some particular examples are related to multi-parametric quantum deformations of the harmonic oscillators.

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English version:
Theoretical and Mathematical Physics, 1993, 94:2, 150–165

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Received: 11.09.1992
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Citation: A. T. Filippov, A. P. Isaev, A. B. Kurdikov, “Paragrassmann differential calculus”, TMF, 94:2 (1993), 213–231; Theoret. and Math. Phys., 94:2 (1993), 150–165

Citation in format AMSBIB
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\by A.~T.~Filippov, A.~P.~Isaev, A.~B.~Kurdikov
\paper Paragrassmann differential calculus
\jour TMF
\yr 1993
\vol 94
\issue 2
\pages 213--231
\mathnet{http://mi.mathnet.ru/tmf1418}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1221732}
\zmath{https://zbmath.org/?q=an:0822.58003}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 2
\pages 150--165
\crossref{https://doi.org/10.1007/BF01019327}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LZ24300004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Daniel C. Cabra, Enrique F. Moreno, A. Tanasă, “Para-Grassmann Variables and Coherent States”, SIGMA, 2 (2006), 087, 8 pp.  mathnet  crossref  mathscinet  zmath
    2. Toufik Mansour, Matthias Schork, “On Linear Differential Equations Involving a Para-Grassmann Variable”, SIGMA, 5 (2009), 073, 26 pp.  mathnet  crossref  mathscinet
    3. Semikhatov A.M., “A Heisenberg Double Addition to the Logarithmic Kazhdan-Lusztig Duality”, Letters in Mathematical Physics, 92:1 (2010), 81–98  crossref  mathscinet  zmath  adsnasa  isi
    4. Ghader Najarbashi, Yusef Maleki, “Entanglement of Grassmannian Coherent States for Multi-Partite $n$-Level Systems”, SIGMA, 7 (2011), 011, 11 pp.  mathnet  crossref  mathscinet
    5. Yusef Maleki, “Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian $q$-Oscillator and their Entanglement”, SIGMA, 7 (2011), 084, 20 pp.  mathnet  crossref  mathscinet
    6. Semikhatov A.M., “Heisenberg Double H(B*) as a Braided Commutative Yetter-Drinfeld Module Algebra Over the Drinfeld Double”, Comm Algebra, 39:5 (2011), 1883–1906  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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