1993/07/26 by Füsun Akman, Fusun Akman, Akman, Fusun
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/9307153
19 pages, submitted to the Proceedings of the Conference on Quantum Topology, Kansas State University, Manhattan, KS, 24-28 March 1993
arxiv created 1993/07/26 · arxiv updated 2009/11/30
It is typical for a semi-infinite cohomology complex associated with a graded Lie algebra to occur as a vertex operator (or chiral) superalgebra where all the standard operators of cohomology theory, in particular the differential, are modes of vertex operators (fields). Although vertex operator superalgebras -with the inherent Virasoro action- are regarded as part of Conformal Field Theory (CFT), a VOSA may exhibit a square-zero operator (often, but not always, the semi-infinite cohomology differential) for which the Virasoro algebra acts trivially in the cohomology. Capable of shedding its CFT features, such a VOSA is called a ``topological chiral algebra'' (TCA). We investigate the semi-infinite cohomology of the vertex operator Weil algebra and indicate a number of differentials which give rise to TCA structures.