L(Infinity) Structures on Spaces of Low Dimension
No Thumbnail Available
Files
Date
2004-04-14
Authors
Journal Title
Series/Report No.
Journal ISSN
Volume Title
Publisher
Abstract
L(Infinity) structures are natural generalizations of Lie algebras, which need satisfy the standard graded Jacobi identity only up to homotopy. They have also been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This dissertation classifies all possible L(Infinity) structures which can be constructed on a Z-graded (characteristic 0) vector space of dimension three or less. It also includes necessary and sufficient conditions under which a space with an L(3) structure is a differential graded Lie algebra. Additionally, it is shown that some of these differential graded Lie algebras possess a nontrivial L(n) structure for higher n.
Description
Keywords
homotopy Lie algebras
Citation
Degree
PhD
Discipline
Mathematics