We provide an explicit quantization of dynamical r-matrices for semisimple Lie algebras,
classified earlier by the third author, which includes the Belavin-Drinfeld r-matrices. We do …

We study classical twists of Lie bialgebra structures on the polynomial current algebra gu,
where g is a simple complex finite-dimensional Lie algebra. We focus on the structures …

We study the multi-parameter quantum groups defined by the generators and relations
associated with symmetrizable generalized Cartan matrices, together with their …

The notion of a quasideterminant and a quasiminor of a matrix A=(a_ {ij}) with not
necessarily commuting entries was introduced recently by I. Gelfand and the second author …

On twisting solutions to the Yang-Baxter equation Page 1 ON TWISTING SOLUTIONS TO THE
YANG-BAXTER EQUATION*) PP KULISH St.-Petersburg Department of the Steklov …

The universal R-matrix for a class of esoteric (nonstandard) quantum groups U q (gl (2N+ 1))
is constructed as a twisting of the universal R-matrix RS of the Drinfeld–Nimbo quantum …

In this article we discuss the Belavin-Drinfeld quantum groups, one of the most fascinating
and elusive classes of non-standard quantum groups. Belavin and Drinfeld classified all non …

We introduce a new class of 2-cocycles defined explicitly on the generators of certain
multiparameter standard quantum groups. These allow us, through the process of twisting …

We prove the GGS conjecture (1993), due to Gerstenhaber, Giaquinto, and Schack, which
gives a particularly simple explicit quantization of classical r-matrices for Lie algebras gl (n) …

We find the general solution to the twisting equation in the tensor bialgebra T (R) of an
associative unital ring R viewed as that of fundamental representation for a universal …