Post-Lie Algebra Structures on the Witt Algebra

On the Restricted Lie Algebra Structure for the Witt Lie Algebra in Finite Characteristic

The Lie algebra W = DerA is called the Witt algebra. It consists of “vector fields” f∂, f ∈ A. In particular, dimF W = dimF A = p. As any Lie algebra of derivations of a commutative algebra over F, W has a canonical structure of a restricted Lie algebra. Recall that a restricted Lie algebra is a Lie algebra over F with an additional unary (in general, non-linear) operation g 7→ g satisfying the...

PostLie algebra structures on the Lie Algebra SL(2,Ca)

L∞ algebra structures of Lie algebra deformations

In this paper,we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into Strong homotopy Lie algebra or L∞ algebra. All such obstructions have been transfered to the revelvant L∞ algebras which contain only three terms.

Lie triple derivation algebra of Virasoro-like algebra

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

Differential Hopf algebra structures on the universal enveloping algebra of a lie algebra

We discuss a method to construct a De Rham complex (diierential algebra) of Poincar e-Birkhoo-Witt-type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a diierential Hopf algebra that naturally extends the Hopf algebra structure of U(g). The construction of such diierential structures is interpreted in terms of colour Lie superalgebras.