L(Infinity) Structures on Spaces of Low Dimension
Title: | L(Infinity) Structures on Spaces of Low Dimension |
Author: | Daily, Marilyn Elizabeth |
Advisors: | Kailash Misra, Committee Member Ron Fulp, Committee Member Jim Stasheff, Committee Member Tom Lada, Committee Chair |
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. |
Date: | 2004-04-14 |
Degree: | PhD |
Discipline: | Mathematics |
URI: | http://www.lib.ncsu.edu/resolver/1840.16/5282 |
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