L(Infinity) Structures on Spaces of Low Dimension

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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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