Poisson-Lie groupoids and the contraction procedure

• Autorzy: Kenny De Commer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16S80: Deformations of rings
• 53D17: Poisson manifolds; Poisson groupoids and algebroids
• 17B62: Lie bialgebras; Lie coalgebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 106
• Numer: 1
• Strony: 35-46

Daty

wydano

2015

Twórcy

autor

Kenny De Commer

• Department of Mathematics, Vrije Universiteit Brussel VUB, B-1060 Brussels, Belgium

Identyfikatory

DOI

10.4064/bc106-0-3