TL;DR
This paper reviews recent advances in BV formalism, highlighting its geometric structures as Q- and QP-manifolds, and illustrates their applications to Lie algebroids and Courant algebroids.
Contribution
It summarizes the mathematical structures underlying BV formalism and demonstrates their realization through Lie and Courant algebroids.
Findings
BV formalism is characterized by Q- and QP-manifolds.
Lie algebroids are examples of Q-manifolds.
BV actions are constructed from Lie and Courant algebroid structures.
Abstract
Recent developments of Batalin-Vilkovisky (BV) formalism and related geometry are reviewed. Mathematical structures of BV formalism are summarized as a Q-manifold and a QP-manifold. Lie algebras, Lie algebroids and other higher algebroids are explained as typical examples of Q- and QP-manifolds. Finally, the BV action functionals are constructed by geometric structures of Lie algebroids and Courant algebroids.
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