Semiinfinite cohomology (or semi-infinite cohomology) is a mathematical counterpart of BRST reduction. The name corresponds to working with resolutions involving certain subspaces of infinite-dimensional Fock representations which correspond to half-dimensional splittings.
In mathematics it is introduced by Boris Feigin.
B. Feigin, D. Fuchs, Verma modules over the Virasoro algebra, Topology (Leningrad, 1982), p. 230–245, Lecture Notes in Math. 1060, Springer, Berlin, 1984.
A. Pressley, G. Segal, Loop groups, Oxford Math. Monographs, 1986.
Leonid Positselski, Homological algebra of semimodules and semicontramodules. Semi-infinite homological algebra of associative algebraic structures, arxiv/0708.3398
A.V. Stoyanovsky, B.L. Feigin, Функциональные модели представлений алгебр токов и полубесконечные клетки Шуберта, Функц. анализ и его прил., 1994, 28 (1), с. 68–90, pdf; Engl. transl.: Functional models for representations of current algebras and semi-infinite Schubert cells, Funct. Anal. Appl. 28 (1), 55–72 (1994), doi
S. Arkhipov, Semi-infinite cohomology of associative algebras and bar-duality, Internat. Math. Research Notices 1997, 17, 833–863. q-alg/9602013
S. Arkhipov, Semi-infinite cohomology of Tate Lie algebras, Moscow Math. Journ. 2, n.1, 35–40, 2002, math.QA/0003015
A. Sevostyanov. Semi-infinite cohomology and Hecke algebras. Advances Math. 159, n.1, p. 83–141, 2001, math.RA/0004139
Boris Feigin, Edward Frenkel, Semi-infinite Weil complex and the Virasoro algebra, Comm. Math. Phys. 137:3 (1991), 617-639 euclid
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