L -Lie Algebroids over Topological Ringed Spaces

Abstract

Lie algebroids over a topological ringed space provides a unified framework to study various geometric structures. This geometric concept is intimately connected with well-known algebraic structures, including Gerstenhaber algebras and Batalin-Vilkovisky algebras. We introduce more general concepts such as L -Lie algebroids and A -Gerstenhaber algebras, associated with a given Lie algebroid L and Gerstenhaber algebra A over a topological ringed space, respectively. Following this, we explore how several standard correspondences extend within this broader framework.