Work

Deformations of Vector Fields and Hamiltonian Vector Fields on the Plane

Year: 1995

Type: article

Abstract: For the Lie algebras L 1 ( H ( 2 ) ) {L_1}(H(2)) and L 1 ( W ( 2 ) ) {L_1}(W(2)) , we study their infinitesimal deformations and the corresponding global ones. We show that, as in the case of L 1 ( W ( 1 ) ) {L_1}(W(1)) , each integrable infinitesimal deformation of L 1 ( H ( 2 ) ) {L_1}(H(2)) and L 1 ( W ( 2 ) ) {L_1}(W(2)) can be represented by a 2-cocycle that defines a global deformation by means of a trivial extension. We also illustrate that all deformations of L 1 ( H ( 2 ) ) {L_1}(H(2)) arise as restrictions of deformations of L 1 ( W ( 2 ) ) {L_1}(W(2)) .

Source: Mathematics of Computation

DOI: 10.1090/s0025-5718-1995-1297480-5

Authors: Nico van den Hijligenberg, Youri Kotchetkov, Gerhard Post

Institutions: Centrum Wiskunde & Informatica, American Mathematical Society

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

OpenAlex ID: W2143730518