Comparison of 3-dimensional Z-graded and Z_2-graded L_Infinity algebras

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dc.creatorDaily, Marilyn
dc.creatorFialowski, Alice
dc.creatorPenkava, Michael
dc.date2006-06-26
dc.date.accessioned2026-07-07T07:17:41Z
dc.date.available2026-07-07T07:17:41Z
dc.descriptionThis article explores L_Infinity structures -- also known as 'strongly homotopy Lie algebras' -- on 3-dimensional vector spaces with both Z- and Z_2-gradings. Since the Z-graded L_Infinity algebras are special cases of Z_2-graded algebras in the induced Z_2-grading, there are generally fewer Z-graded L_Infinity structures on a given space. On the other hand, only degree zero automorphisms, rather than just even automorphisms, are used to determine equivalence in a Z-graded space. We therefore find nontrivial examples in which the map from the Z-graded moduli space to the Z_2-graded moduli space is bijective, injective but not surjective, or surjective but not injective. Additionally, we study how the codifferentials in the moduli spaces deform into other nonequivalent codifferentials, which gives each moduli space a sort of topology.
dc.description31 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0606644
dc.identifierhttp://arxiv.org/abs/math/0606644
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114030
dc.subjectQuantum Algebra
dc.subject14D15,13D10,14B12,16S80,16E40,17B55,17B70
dc.titleComparison of 3-dimensional Z-graded and Z_2-graded L_Infinity algebras
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