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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 347, Pages 187–213
(Mi znsl81)
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Parabolic twists for linear algebras $A_{n-1}$
V. D. Lyakhovsky Saint-Petersburg State University
Abstract:
New solutions of twist equations for universal enveloping algebras $U(A_{n-1})$ are found. They can be presented as products of full chains of extended Jordanian twists $\mathcal F_{\widehat{ch}}$, Abelian factors (“rotations”) $\mathcal F^R$ and sets of quasi-Jordanian twists $\mathcal F^{\widehat J}$. The latter are the generalizations of Jordanian twists (with carrier $b^2$) for special deformed extensions of the Hopf algebra $U(b^2)$. The carrier subalgebra $g_{\mathcal P}$ for the composition $\mathcal F_{\mathcal P}=\mathcal F^{\widehat J}\mathcal F^R\mathcal F_{\widehat{ch}}$ is a nonminimal parabolic subalgebra in $A_{n-1}$, $g_{\mathcal P}\cap\mathbb N_g^-\ne\varnothing$. The parabolic twisting elements $\mathcal F_{\mathcal P}$ are obtained in the explicit form. The details of the construction are illustrated by considering the examples $n=4$ and $n=11$.
Received: 13.07.2007
Citation:
V. D. Lyakhovsky, “Parabolic twists for linear algebras $A_{n-1}$”, Questions of quantum field theory and statistical physics. Part 20, Zap. Nauchn. Sem. POMI, 347, POMI, St. Petersburg, 2007, 187–213; J. Math. Sci. (N. Y.), 151:2 (2008), 2907–2923
Linking options:
https://www.mathnet.ru/eng/znsl81 https://www.mathnet.ru/eng/znsl/v347/p187
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Abstract page: | 185 | Full-text PDF : | 48 | References: | 51 |
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