L ∞-Algebra Actions

Authors

Rajan Amit Mehta, Pennsylvania State UniversityFollow
Marco Zambon, Universidad Autónoma de Madrid

Document Type

Article

Publication Date

12-1-2012

Publication Title

Differential Geometry and its Application

Abstract

We define the notion of action of an L -algebra g on a graded manifold M, and show that such an action corresponds to a homological vector field on g[1]×M of a specific form. This generalizes the correspondence between Lie algebra actions on manifolds and transformation Lie algebroids. In particular, we consider actions of g on a second L -algebra, leading to a notion of "semidirect product" of L -algebras more general than those we found in the literature.

Keywords

Action, Extension, Graded manifold, L -algebra ∞, Lie algebroid

Volume

30

Issue

6

First Page

576

Last Page

587

DOI

10.1016/j.difgeo.2012.07.006

ISSN

09262245

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit and Zambon, Marco, "L ∞-Algebra Actions" (2012). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/90