Unimodular L-infinity algebras

Details Unimodular L-infinity algebras Unimodular L-infinity algebras

2008-03-12

arxiv.org/abs/0803.1763v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a unimodular L-infinity algebra. Such a structure corresponds to a homological vector field on V together with an invariant measure. We present explicit formulae for homotopy transferred structures, define the deformation complex and give a cohomological obstruction to the extension of an arbitrary structure of finite dimensional L-infinity algebra to a structure of unimodular L-infinity algebra.

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