Strongly Homotopy Lie Algebras of One Even and Two Odd Dimensions

Details Strongly Homotopy Lie Algebras of One Even and Two Odd Dimensions Strongly Homotopy Lie Algebras of One Even and Two Odd Dimensions

2003-08-03

arxiv.org/abs/math/0308016v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many nonequivalent L-infinity examples, in addition to the $Z_2$-graded Lie algebra (or superalgebra) structures, yet the moduli space is simple enough that we can give a complete classification up to equivalence.

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