scholarly journals Left-symmetric bialgebroids and their corresponding Manin triples

2018 ◽  
Vol 59 ◽  
pp. 91-111 ◽  
Author(s):  
Jiefeng Liu ◽  
Yunhe Sheng ◽  
Chengming Bai
Keyword(s):  
Manin Triples

scholarly journals On Lie bialgebroid crossed modules

2021 ◽  
Vol 32 (04) ◽  
pp. 2150021
Author(s):  
Honglei Lang ◽  
Yu Qiao ◽  
Yanbin Yin
Keyword(s):  
Lie Algebroid ◽  
Dirac Structures ◽  
Crossed Modules ◽  
Manin Triples

We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence between such Lie bialgebroid crossed modules and co-quadratic Manin triples [Formula: see text] is established, where [Formula: see text] is a co-quadratic Lie algebroid and [Formula: see text] is a pair of transverse Dirac structures in [Formula: see text].

scholarly journals Manin triples for Lie bialgebroids

1997 ◽  
Vol 45 (3) ◽  
pp. 547-574 ◽  
Author(s):  
Zhang-Ju Liu ◽  
Alan Weinstein ◽  
Ping Xu
Keyword(s):  
Manin Triples

scholarly journals Formal Pseudodifferential Operators in One and Several Variables, Central Extensions, and Integrable Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Jarnishs Beltran ◽  
Enrique G. Reyes
Keyword(s):  
Lie Algebras ◽  
Nonlinear Equations ◽  
Integrable Systems ◽  
Differential Operators ◽  
Pseudodifferential Operators ◽  
Central Extensions ◽  
Several Variables ◽  
Zero Curvature ◽  
Manin Triples

We review some aspects of the theory of Lie algebras of (twisted and untwisted) formal pseudodifferential operators in one and several variables in a general algebraic context. We focus mainly on the construction and classification of nontrivial central extensions. As applications, we construct hierarchies of centrally extended Lie algebras of formal differential operators in one and several variables, Manin triples and hierarchies of nonlinear equations in Lax and zero curvature form.

scholarly journals QUASI FROBENIUS LIE ALGEBRAS CONSTRUCTION OF N=4 SUPERCONFORMAL FIELD THEORIES

1996 ◽  
Vol 11 (06) ◽  
pp. 445-461 ◽  
Author(s):  
S.E. PARKHOMENKO
Keyword(s):  
Lie Algebras ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Finite Dimensional ◽  
Manin Triples ◽  
Finite Dimensional Lie Algebras

The Manin triples construction of N =4 superconformal field theories is considered. A correspondence between quasi Frobenius finite-dimensional Lie algebras and N =4 Virasoro superalgebras is established.

scholarly journals CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS

2002 ◽  
Vol 17 (07) ◽  
pp. 429-434 ◽  
Author(s):  
LADISLAV HLAVATÝ ◽  
LIBOR ŠNOBL
Keyword(s):  
Sigma Models ◽  
Two Dimensional ◽  
Drinfeld Double ◽  
Manin Triples ◽  
Dual Models

Four-dimensional Manin triples and Drinfeld doubles are classified and the corresponding two-dimensional Poisson–Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two nontrivially different Manin triples is presented.

scholarly journals Another approach to Hom-Lie bialgebras via Manin triples

2020 ◽  
Vol 48 (7) ◽  
pp. 3109-3132 ◽  
Author(s):  
Yi Tao ◽  
Chengming Bai ◽  
Li Guo
Keyword(s):  
Lie Bialgebras ◽  
Manin Triples

scholarly journals Coideal algebras from twisted Manin triples

2012 ◽  
Vol 62 (10) ◽  
pp. 2009-2023 ◽  
Author(s):  
S. Belliard ◽  
N. Crampé
Keyword(s):  
Manin Triples
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