3,119 research outputs found
Classification of Lie bialgebras over current algebras
In the present paper we present a classification of Lie bialgebra structures
on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional
Lie algebra.Comment: 26 page
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
Classification of Low Dimensional Lie Super-Bialgebras
A thorough analysis of Lie super-bialgebra structures on Lie super-algebras
osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic
computations and a subsequent identification of equivalent structures is
applied. In all the cases Poisson-Lie brackets on supergroups are found.
Possibility of quantizing them in order to obtain quantum groups is discussed.
It turns out to be straightforward for all but one structures for super-E(2)
group.Comment: 15 pages, LaTe
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
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
Cremmer-Gervais r-matrices and the Cherednik Algebras of type GL2
We give an intepretation of the Cremmer-Gervais r-matrices for sl(n) in terms
of actions of elements in the rational and trigonometric Cherednik algebras of
type GL2 on certain subspaces of their polynomial representations. This is used
to compute the nilpotency index of the Jordanian r-matrices, thus answering a
question of Gerstenhaber and Giaquinto. We also give an interpretation of the
Cremmer-Gervais quantization in terms of the corresponding double affine Hecke
algebra.Comment: 6 page
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