Reduction of local Lie algebra structures

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

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.

The Lie Algebra of Local Killing Fields

!We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. As an application, we provide a local classification of the types of surfaces that admit the various possible Lie algebras of local Killing fields, in terms of the Gaussian cu...

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