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Fundam. Prikl. Mat., 2005, Volume 11, Issue 2, Pages 185–208 (Mi fpm821)  

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

The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix

V. A. Stukopin

Don State Technical University

Abstract: The Yangian double $DY(A(m,n))$ of the Lie superalgebra $A(m,n)$ is described in terms of generators and defining relations. We prove the triangular decomposition for Yangian $Y(A(m,n))$ and its quantum double $DY(A(m,n))$ as a corollary of the PBW theorem. We introduce normally ordered bases in the Yangian and its dual Hopf superalgebra in the quantum double. We calculate the pairing formulas between the elements of these bases. We obtain the formula for the universal $R$-matrix of the Yangian double. The formula for the universal $R$-matrix of the Yangian, which was introduced by V. Drinfel'd, is also obtained.

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English version:
Journal of Mathematical Sciences (New York), 2007, 142:2, 1989–2006

Bibliographic databases:

UDC: 512.667.7+512.554.32

Citation: V. A. Stukopin, “The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix”, Fundam. Prikl. Mat., 11:2 (2005), 185–208; J. Math. Sci., 142:2 (2007), 1989–2006

Citation in format AMSBIB
\Bibitem{Stu05}
\by V.~A.~Stukopin
\paper The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 2
\pages 185--208
\mathnet{http://mi.mathnet.ru/fpm821}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2157938}
\zmath{https://zbmath.org/?q=an:1072.17008}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 142
\issue 2
\pages 1989--2006
\crossref{https://doi.org/10.1007/s10958-007-0106-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947368313}


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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. Stukopin V.A., “The Yangian double of the Lie superalgebra $A(m,n)$”, Funct. Anal. Appl., 40:2 (2006), 155–158  mathnet  crossref  mathscinet  zmath  isi  elib
    2. V. A. Stukopin, “O predstavleniyakh yangiana superalgebry Li $\mathfrak{sl}(1,2)$”, Vladikavk. matem. zhurn., 13:3 (2011), 53–63  mathnet
    3. V. A. Stukopin, “The Yangian of the strange Lie superalgebra and its quantum double”, Theoret. and Math. Phys., 174:1 (2013), 122–133  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. A. Stukopin, “Representations of the Yangian of a Lie superalgebra of type $A(m,n)$”, Izv. Math., 77:5 (2013), 1021–1043  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. A. Stukopin, “Isomorphism of the Yangian $Y_{\hbar}(A(m,n))$ of the special linear Lie superalgebra and the quantum loop superalgebra $U_{\hbar}(LA(m,n))$”, Theoret. and Math. Phys., 198:1 (2019), 129–144  mathnet  crossref  crossref  adsnasa  isi  elib
    6. V. A. Stukopin, “Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra”, Theoret. and Math. Phys., 204:3 (2020), 1227–1243  mathnet  crossref  crossref  isi
  • Фундаментальная и прикладная математика
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