Some Classical and Quantum Algebras

Abstract

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.KeywordsVertex OperatorOperator AlgebraCommutative AlgebraOperator Product ExpansionQuantum OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.