Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Cohomology of nilpotent subalgebras of affine Lie algebras

Author: A. Fialowski
Journal: Proc. Amer. Math. Soc. 122 (1994), 71-77
MSC: Primary 17B56
MathSciNet review: 1198456
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We compute the cohomology of the maximal nilpotent Lie algebra of an affine Lie algebra $ \hat{\mathfrak{g}}$ with coefficients in modules of functions on the circle with values in a representation space of $ \mathfrak{g}$. These modules are not highest weight modules and are somewhat similar to the adjoint representation.

References [Enhancements On Off] (What's this?)

  • [A] L. L. Avramov, On the Hopf algebra of a local ring, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 253-277. MR 0349816 (50:2309)
  • [F] B. L. Feigin, Cohomology of groups and algebras of flows, Russian Math. Surveys 35 (1980), 239-240. MR 571663 (81h:17018)
  • [FF] B. L. Feigin and A. Fialowski, The cohomology of nilpotent algebras of flows, Soviet Math. Dokl. 28 (1983), no. 1, 178-181.
  • [FR] B. L. Feigin. and V. S. Retach, Cohomology of some Lie algebras and superalgebras of vector fields, Russian Math. Surveys 37 (1982), no. 2, 251-252. MR 650787 (83m:58083)
  • [Fu] D. B. Fuchs, Cohomology of infinite dimensional Lie algebras, Translation from Russian, Consultants Bureau, New York, 1986. MR 874337 (88b:17001)
  • [G] H. Garland, Dedekind's $ \zeta $-function and the cohomology of infinite dimensional Lie algebras, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2493-2495. MR 0387361 (52:8204)
  • [GL] H. Garland and J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), 37-76. MR 0414645 (54:2744)
  • [K] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil Theorem, Ann. of Math. (2) 74 (1961), 329-387. MR 0142696 (26:265)
  • [L] J. Lepowsky, Generalized Verma modules, loop space cohomology and Macdonald-type identities, Ann. Sci. École Norm. Sup. (4) 12 (1979), 169-235. MR 543216 (81a:17004)
  • [M] J. C. Moore, Algebre homologique et homologie espace classificants, Sem. H. Cartan, Expose 7, 1959/60.
  • [S] J.-P. Serre, Groupes d'homotopie et classes de groupes abeliens, Ann. of Math. (2) 58 (1953), 258-294. MR 0059548 (15:548c)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B56

Retrieve articles in all journals with MSC: 17B56

Additional Information

Keywords: Affine Lie algebra, adjoint representation, Lie algebra cohomology, spectral sequence
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society