L(Infinity) Structures on Spaces of Low Dimension

homotopy Lie algebras

Daily, Marilyn Elizabeth ; Kailash Misra, Committee Member,Ron Fulp, Committee Member,Jim Stasheff, Committee Member,Tom Lada, Committee Chair,Daily, Marilyn Elizabeth ; Kailash Misra ; Committee Member ; Ron Fulp ; Committee Member ; Jim Stasheff ; Committee Member ; Tom Lada ; Committee Chair

University:North Carolina State University

关键词: homotopy Lie algebras;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5282/etd.pdf?sequence=2&isAllowed=y

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【 摘 要 】

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.