Derived brackets and sh Leibniz algebras

Details Derived brackets and sh Leibniz algebras Derived brackets and sh Leibniz algebras

2009-01-31

arxiv.org/abs/0902.0044v7

Mathematics

Quantum Algebra

The Final Version

Scientific paper

We develop a general framework for the construction of various derived brackets. We show that suitably deforming the differential of a graded Leibniz algebra extends the derived bracket construction and leads to the notion of strong homotopy (sh) Leibniz algebra. We discuss the connections among homotopy algebra theory, deformation theory and derived brackets. We prove that the derived bracket construction induces a map from suitably defined deformation theory equivalence classes to the isomorphism classes of sh Leibniz algebras.

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