Commutative quantum operator algebras (Q1896837)

The authors generalize the notion of vertex operators to that of ``quantum operators'', which are abstract series of operators (endomorphisms) on a \(\mathbb{Z}\)-doubly-graded vector space and are not required to be generated by the vectors in the space. The operations that they define for two quantum operators are extracted from part of a certain component form of the Jacobi identity [\textit{I. Frenkel}, \textit{J. Lepowsky} and \textit{A. Meurman}, Vertex operator algebras and the Monster, Pure Appl. Math. 134, Academic Press (1988; Zbl 0674.17001)]. The authors prove some properties of these operations, which are closely related to the Jacobi identity.