Poisson-Lie groupoids and the contraction procedure

Kenny De Commer. "Poisson-Lie groupoids and the contraction procedure." Banach Center Publications 106.1 (2015): 35-46. <http://eudml.org/doc/281616>.

@article{KennyDeCommer2015,
abstract = {On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these Lie algebras. This will give a bundle of central extensions of the above Lie algebras with a Lie bialgebroid structure having transversal component. We consider as well the dual Lie bialgebroid, which is in a sense easier to understand, and whose integration can be explicitly presented.},
author = {Kenny De Commer},
journal = {Banach Center Publications},
keywords = {Lie algebras; scaling parameter; Lie bialgebroid},
language = {eng},
number = {1},
pages = {35-46},
title = {Poisson-Lie groupoids and the contraction procedure},
url = {http://eudml.org/doc/281616},
volume = {106},
year = {2015},
}

TY - JOUR
AU - Kenny De Commer
TI - Poisson-Lie groupoids and the contraction procedure
JO - Banach Center Publications
PY - 2015
VL - 106
IS - 1
SP - 35
EP - 46
AB - On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these Lie algebras. This will give a bundle of central extensions of the above Lie algebras with a Lie bialgebroid structure having transversal component. We consider as well the dual Lie bialgebroid, which is in a sense easier to understand, and whose integration can be explicitly presented.
LA - eng
KW - Lie algebras; scaling parameter; Lie bialgebroid
UR - http://eudml.org/doc/281616
ER -