3,126 research outputs found
Chains of Frobenius subalgebras of so(M) and the corresponding twists
Chains of extended jordanian twists are studied for the universal enveloping
algebras U(so(M)). The carrier subalgebra of a canonical chain F cannot cover
the maximal nilpotent subalgebra N(so(M)). We demonstrate that there exist
other types of Frobenius subalgebras in so(M) that can be large enough to
include N(so(M)). The problem is that the canonical chains F do not preserve
the primitivity on these new carrier spaces. We show that this difficulty can
be overcome and the primitivity can be restored if one changes the basis and
passes to the deformed carrier spaces. Finally the twisting elements for the
new Frobenius subalgebras are explicitly constructed. This gives rise to a new
family of universal R-matrices for orthogonal algebras. For a special case of g
= so(5) and its defining representation we present the corresponding matrix
solution of the Yang-Baxter equation.Comment: 17 pages, Late
New -Matrices for Lie Bialgebra Structures over Polynomials
For a finite dimensional simple complex Lie algebra , Lie
bialgebra structures on and were
classified by Montaner, Stolin and Zelmanov. In our paper, we provide an
explicit algorithm to produce -matrices which correspond to Lie bialgebra
structures over polynomials
Twists in U(sl(3)) and their quantizations
The solution of the Drinfeld equation corresponding to the full set of
different carrier subalgebras in sl(3) are explicitly constructed. The obtained
Hopf structures are studied. It is demonstrated that the presented twist
deformations can be considered as limits of the corresponding quantum analogues
(q-twists) defined for the q-quantized algebras.Comment: 31 pages, Latex 2e, to be published in Journ. Phys. A: Math. Ge
Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras
In this paper we continue to study Belavin-Drinfeld cohomology introduced in
arXiv:1303.4046 [math.QA] and related to the classification of quantum groups
whose quasi-classical limit is a given simple complex Lie algebra. Here we
compute Belavin-Drinfeld cohomology for all non-skewsymmetric -matrices from
the Belavin-Drinfeld list for simple Lie algebras of type , , and .Comment: 17 page
Q-power function over Q-commuting variables and deformed XXX, XXZ chains
We find certain functional identities for the Gauss q-power function of a sum
of q-commuting variables. Then we use these identities to obtain two-parameter
twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian
Y(sl_2). We determine the corresponding deformed trigonometric and rational
quantum R-matrices, which then are used in the computation of deformed XXX and
XXZ Hamiltonians.Comment: LaTeX, 12 page
Construction of a universal twist element from an R-matrix
We propose a method for construction of a universal twist element based on a constant quasi-classical unifary matrix solution of the Yang-Baxter equation. The method is applied to few known R-matrices corresponding to Lie (super) algebras of rank one. Bibliography: 13 titles. \ua9 2005 Springer Science+Business Media, Inc
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
We study classical twists of Lie bialgebra structures on the polynomial
current algebra , where is a simple complex
finite-dimensional Lie algebra. We focus on the structures induced by the
so-called quasi-trigonometric solutions of the classical Yang-Baxter equation.
It turns out that quasi-trigonometric -matrices fall into classes labelled
by the vertices of the extended Dynkin diagram of . We give
complete classification of quasi-trigonometric -matrices belonging to
multiplicity free simple roots (which have coefficient 1 in the decomposition
of the maximal root). We quantize solutions corresponding to the first root of
.Comment: 41 pages, LATE
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