  We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several
classical examples from differential geometry and Lie theory. We introduce the
notion of a quantum operator algebra (QOA) as a generalization of a classical
operator algebra. In some examples, we view a QOA as a deformation of a
commutative algebra. We then review the notion of a vertex operator algebra
(VOA) and show that a vertex operator algebra is a QOA with some additional
structures. Finally, we establish a connection between BV algebras and VOAs.

High Energy Physics - Theory;Quantum Algebra