semiinfinite cohomology

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

Revised on September 5, 2014 18:26:14 by Zoran Škoda (