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 Zap. Nauchn. Sem. POMI, 2007, Volume 347, Pages 187–213 (Mi znsl81)

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 $n=11$.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:2, 2907–2923

Bibliographic databases:

UDC: 517.9, 512.81
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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

Citation in format AMSBIB
\Bibitem{Lya07} \by V.~D.~Lyakhovsky \paper Parabolic twists for linear algebras $A_{n-1}$ \inbook Questions of quantum field theory and statistical physics. Part~20 \serial Zap. Nauchn. Sem. POMI \yr 2007 \vol 347 \pages 187--213 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl81} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2458892} \transl \jour J. Math. Sci. (N. Y.) \yr 2008 \vol 151 \issue 2 \pages 2907--2923 \crossref{https://doi.org/10.1007/s10958-008-9008-4} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249138662}