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Some cohomology operators in 2-D field theory. (English) Zbl 1036.81514

Yetter, David N. (ed.), Proceedings of the conference on quantum topology, Manhattan, KS, USA, March 24–28, 1993. Singapore: World Scientific (ISBN 981-02-1727-7/hbk). 1-19 (1994).
The author gives a survey of the results of her Ph.D. thesis. So far semi-infinite cohomology is a well-established tool in both modern mathematics and theoretical physics (where it is called “BRST cohomology). The new approach developed by the author is the characterization of the semi-infinite cohomology differential as an associative algebra derivation which is generically of square zero.
For the entire collection see [Zbl 0869.00040].

MSC:

81T45 Topological field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T70 Quantization in field theory; cohomological methods
17B56 Cohomology of Lie (super)algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B69 Vertex operators; vertex operator algebras and related structures
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