Results 41 to 50 of about 83 (77)

Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation. [PDF]

Transform Groups
Huang H, Nguyen VC, Ure C, Vashaw KB, Veerapen P, Wang X.   +5 more
europepmc   +1 more source

Weak Lie 2-bialgebras

Journal of Geometry and Physics, 2013
We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term $L_\infty$-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.
Zhuo Chen
exaly   +3 more sources

On the Associative Analog of Lie Bialgebras

Journal of Algebra, 2001
This paper deals with \(\varepsilon\)-bialgebras, that is associative algebras equipped with coalgebra structures such that the comultiplications are derivations. The goal is to connect these objects with Lie bialgebras. Given an element \(r\in A\otimes A\), the author defines \({\mathbf A}(r)\), the left-hand side of the ``associative Yang-Baxter ...
exaly   +2 more sources

On Quantizable Odd Lie Bialgebras [PDF]

Letters in Mathematical Physics, 2016
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so called ...
Anton Khoroshkin, Thomas Willwacher
exaly   +5 more sources

The Variety of Lie Bialgebras

Journal of Lie Theory, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CICCOLI, Nicola, GUERRA, Lucio
openaire   +3 more sources

Lie Bialgebras with Triality and Mal’tsev Bialgebras

Algebra and Logic, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

The Construction of Hom-Lie Bialgebras

Journal of Lie Theory, 2010
A Hom-Lie algebra is a triple consisting of a vector space \(L\), a skew-symmetric bracket \([\;,\,\;]\) and a linear endomorphism \(\alpha: L\to L\), satisfying the modified Jacobi identity \[ [[x,y],\alpha(z)]+[[y,z],\alpha(x)]+[[z,x],\alpha(y)]=0. \] If the endomorphism \(\alpha\) preserves the bracket, then one speaks of a multiplicative Hom-Lie ...
Chen, Yuanyuan, Wang, Yong, Zhang, Liangyun   +2 more
openaire   +2 more sources

Quantization of triangular Lie bialgebras

Czechoslovak Journal of Physics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dolgushev, V. A., Isaev, A. P., Lyakovich, S. L., Sharapov, A. A.   +3 more
openaire   +2 more sources

Formality Theorem for Quantizations of Lie Bialgebras [PDF]

Letters in Mathematical Physics, 2015
The title of the paper has been changed and made more precise.
S A Merkulov
exaly   +5 more sources

Lie comodules and the constructions of Lie bialgebras

Science in China Series A: Mathematics, 2008
Let \((C,d)\) be a Lie coalgebra over a field of characteristic not two. A counit for \(C\) is a non-zero element \(e\) of \(C^*\) such that \((e \otimes I)d=0\). Let \((C,d)\) be a Lie coalgebra with counit \(e\), \((M,s)\) a left \(C\)-Lie comodule, \(F:M\to M\) given by \(F(m)=\sum e(m_{(-1)})m_{(0)}\), where \(s(m)= \sum m_{(-1)}\otimes m_{(0 ...
exaly   +2 more sources