RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (244 kB)
References: PDF file   HTML file

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} 

• http://mi.mathnet.ru/eng/fpm821
• http://mi.mathnet.ru/eng/fpm/v11/i2/p185

 SHARE:

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. Stukopin V.A., “The Yangian double of the Lie superalgebra $A(m,n)$”, Funct. Anal. Appl., 40:2 (2006), 155–158
2. V. A. Stukopin, “O predstavleniyakh yangiana superalgebry Li $\mathfrak{sl}(1,2)$”, Vladikavk. matem. zhurn., 13:3 (2011), 53–63
3. V. A. Stukopin, “The Yangian of the strange Lie superalgebra and its quantum double”, Theoret. and Math. Phys., 174:1 (2013), 122–133
4. V. A. Stukopin, “Representations of the Yangian of a Lie superalgebra of type $A(m,n)$”, Izv. Math., 77:5 (2013), 1021–1043
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
•  Number of views: This page: 243 Full text: 64 References: 32