9,525 research outputs found
Derived brackets and sh Leibniz algebras
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.Comment: The Final Versio
- …