Classification and versal deformations of L_\infinity algebras on a 2|1-dimensional space

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dc.creatorBodin, Derek
dc.creatorFialowski, Alice
dc.creatorPenkava, Michael
dc.date2004-01-05
dc.date.accessioned2026-07-07T07:49:40Z
dc.date.available2026-07-07T07:49:40Z
dc.descriptionThis article explores \Z_2-graded L_\infinity algebra structures on a 2|1-dimensional vector space. The reader should note that our convention on the parities is the opposite of the usual one, because we define our structures on the symmetric coalgebra of the parity reversion of a space, so our 2|1-dimensional L_\infinity algebras correspond to the usual 1|2-dimensional algebras. We give a complete classification of all structures with a nonzero degree 1 term. We also classify all degree 2 codifferentials, which is the same as a classification of all 1|2-dimensional Z_2-graded Lie algebras. For each of these algebra structures, we calculate the cohomology and a miniversal deformation.
dc.identifierhttps://arxiv.org/abs/math/0401025
dc.identifierhttp://arxiv.org/abs/math/0401025
dc.identifierHomology, Homotopy, Appl. (7), (2005), 55-86.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124937
dc.subjectQuantum Algebra
dc.subjectK-Theory and Homology
dc.subject(14D15; 13D10; 14B12; 16S80; 16E40; 17B55;17B70)
dc.titleClassification and versal deformations of L_\infinity algebras on a 2|1-dimensional space
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