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TMF, 1993, Volume 95, Number 3, Pages 403–417 (Mi tmf1476)  

This article is cited in 1 scientific paper (total in 1 paper)

Minimum deformations of commutative algebra and linear group $GL(n)$

B. M. Zupnik


Abstract: In the algebra of formal series $M_q(x^i)$, the relations of generalized commutativity that preserve the tensor $I_q$ grading and depend on parameters $q(i,k)$ are considered. A norm of the differential calculus on $M_q$ consistent with the $I_q$ grading is chosen. A new construction of a symmetrized tensor product of algebras of the type $M_q(x^i)$ and a corresponding definition of the minimally deformed linear group $QGL(n)$ and Lie algebra $qgl(n)$ are proposed. A study is made of the connection of $QGL(n)$ and $qgl(n)$ with the special matrix algebra $\operatorname {Mat}(n,Q)$, which consists of matrices with noncommuting elements. The deformed determinant in the algebra $\operatorname {Mat}(n,Q)$ is defined. The exponential mapping in the algebra $\operatorname {Mat}(n,Q)$ is considered on the basis of the Campbell–Hausdorff formula.

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English version:
Theoretical and Mathematical Physics, 1993, 95:3, 677–685

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Received: 07.04.1992

Citation: B. M. Zupnik, “Minimum deformations of commutative algebra and linear group $GL(n)$”, TMF, 95:3 (1993), 403–417; Theoret. and Math. Phys., 95:3 (1993), 677–685

Citation in format AMSBIB
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\by B.~M.~Zupnik
\paper Minimum deformations of commutative algebra and linear group $GL(n)$
\jour TMF
\yr 1993
\vol 95
\issue 3
\pages 403--417
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1243405}
\zmath{https://zbmath.org/?q=an:0848.17016}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 95
\issue 3
\pages 677--685
\crossref{https://doi.org/10.1007/BF01017513}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993ML77300001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Akulov, S. A. Duplij, V. V. Chitov, “Differential calculus for $q$-deformed twistors”, Theoret. and Math. Phys., 115:2 (1998), 513–519  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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