Mathematical Exploration of the Intersection Between Extended Schrodinger-Virasoro Lie Algebras and Symplectic Novikov Lie Algebras

TL;DR

This paper explores the mathematical relationship between extended Schr"odinger-Virasoro and Symplectic Novikov Lie algebras, analyzing their structures and potential applications in physics and geometry.

Contribution

It provides a detailed analysis of derivations, central extensions, and automorphisms of the intersection of these two Lie algebras, revealing new structural insights.

Findings

Identification of derivation structures

Classification of central extensions

Insights into automorphism groups

Abstract

This paper presents an in-depth mathematical investigation into the intersection of two advanced Lie algebraic structures: the extended Schr\"odinger-Virasoro Lie algebra (ESVLA) and the Symplectic Novikov Lie algebra (SNLA). By rigorously analyzing their derivations, central extensions, and automorphism groups, we seek to uncover potential synergies and applications linking these distinct algebraic frameworks. The exploration includes detailed proofs, derivations, and calculations, providing new insights into the representation theory of Lie algebras with potential applications in conformal field theory and symplectic geometry.