On spinor vertex operator algebras and their modules (Q1357794)

The author proves a generator theorem ensuring on a vector space \(V\) with a given set of fields \(S\) a structure of (colored) vertex operator algebra. The author also introduces an asymmetric tensor product of two colored vertex operator superalgebras with the same grading and supermap. These results are used for a characterization of a certain class of vertex operator superalgebras generated by fermionic fields. As a consequence the author gives a shorter proof of the Jacobi identity than the ones given in [\textit{A. J. Feingold}, \textit{I. B. Frenkel} and \textit{J. F. Ries}, Spinor construction of vertex operator algebras, triality and \(E_8^{(1)}\), Contemp. Math. 121 (1991; Zbl 0743.17029)] and [\textit{H. Tsukada}, Commun. Algebra 18, 2249-2274 (1990; Zbl 0704.17001)]. The author also gives a characterization of a certain class of twisted irreducible modules for spinor vertex operator algebras.