Free Courant and derived Leibniz pseudoalgebras

Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces

We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this construction to realize the bracket operations on the sections of Courant algebroid...

Homotopy Leibniz Algebras and Derived Brackets

We will discuss a bar/coalgebra construction of strong homotopy Leibniz algebras. We will give a generalized framework of derived bracket construction. We will prove that a deformation derivation of differential graded Leibniz algebra induces a strong homotopy Leibniz algebra by derived bracket method.

Derived brackets and sh Leibniz algebras

We will give a generalized framework of derived bracket construction. It will be shown that a deformation differential provides a strong homotopy (sh) Leibniz algebra structure by derived bracket construction. A relationship between the three concepts, homotopy algebra theory, deformation theory and derived bracket construction, will be discussed. We will prove that the derived bracket construc...

Homotopy Leibniz algebras and derived brackets ( version 2 )

We will give a generalized framework of derived bracket construction. The derived bracket construction provides a method of constructing homotopies. We will prove that a deformation derivation of dg Leibniz algebra (or called dg Loday algebra) induces a strong homotopy Leibniz algebra by the derived bracket method.

Theory of Finite Pseudoalgebras