Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
C Bai, L Guo, X Ni - Communications in Mathematical Physics, 2010 - Springer
We generalize the classical study of (generalized) Lax pairs, the related\mathcal O-
operators and the (modified) classical Yang-Baxter equation by introducing the concepts of …
operators and the (modified) classical Yang-Baxter equation by introducing the concepts of …
Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang–Baxter equation
This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras,
which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric …
which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric …
[PDF][PDF] Topological Lie bialgebra structures and their classification over g [[x]]
This paper is devoted to a classification of topological Lie bialgebra structures on the Lie
algebra g [[x]], where g is a finite-dimensional simple Lie algebra over an algebraically …
algebra g [[x]], where g is a finite-dimensional simple Lie algebra over an algebraically …
Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras
Lu has shown that any dynamical r-matrix for the pair (g, u) naturally induces a Poisson
homogeneous structure on G/U. She also proved that if g is complex simple, u is its Cartan …
homogeneous structure on G/U. She also proved that if g is complex simple, u is its Cartan …
Topological Lie Bialgebras, Manin Triples and Their Classification Over g [[x]]
The main result of the paper is classification of topological Lie bialgebra structures on the
Lie algebra g [[x]], where g is a finite-dimensional simple Lie algebra over an algebraically …
Lie algebra g [[x]], where g is a finite-dimensional simple Lie algebra over an algebraically …
On Rota-Baxter operators of non-zero weight induced by non skew-symmetric solutions of the classical Yang-baxter equation on simple anticommutative algebras
ME Goncharov - arxiv preprint arxiv:1711.02327, 2017 - arxiv.org
arxiv:1711.02327v1 [math.RA] 7 Nov 2017 Page 1 arxiv:1711.02327v1 [math.RA] 7 Nov 2017
On Rota-Baxter operators of non-zero weight induced by non skew-symmetric solutions of the …
On Rota-Baxter operators of non-zero weight induced by non skew-symmetric solutions of the …
Lagrangian Subalgebras and Quasi-trigonometric r-Matrices
I Pop, A Stolin - Letters in Mathematical Physics, 2008 - Springer
It was proved by Montaner and Zelmanov that up to classical twisting Lie bialgebra
structures on gu fall into four classes. Here g is a simple complex finite-dimensional Lie …
structures on gu fall into four classes. Here g is a simple complex finite-dimensional Lie …
Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures
M Goncharov - Communications in Algebra, 2025 - Taylor & Francis
In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a
motivation, we show that there is a natural connection between Rota-Baxter operators of this …
motivation, we show that there is a natural connection between Rota-Baxter operators of this …
The 4th structure
A Stolin, J Yermolova-Magnusson - Czechoslovak Journal of Physics, 2006 - Springer
According to conclusions made by F. Montaner and E. Zelmanov (unpublished), there exist
four Lie bialgebra structures on g [u] up to classical twisting. Therefore we investigated four …
four Lie bialgebra structures on g [u] up to classical twisting. Therefore we investigated four …
Classification of quantum groups and Belavin–Drinfeld cohomologies
In the present article we discuss the classification of quantum groups whose quasi-classical
limit is a given simple complex Lie algebra g g. This problem is reduced to the classification …
limit is a given simple complex Lie algebra g g. This problem is reduced to the classification …