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, The Hopf algebra of a local ring, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 253–277 (Russian). MR 0349816
  • [F] B. L. Feĭgin, Cohomology of groups and of algebras of flows, Uspekhi Mat. Nauk 35 (1980), no. 2(212), 225–226 (Russian). MR 571663
  • [FF] B. L. Feigin and A. Fialowski, The cohomology of nilpotent algebras of flows, Soviet Math. Dokl. 28 (1983), no. 1, 178-181.
  • [FR] V. S. Retakh and B. L. Feĭgin, Cohomology of some Lie algebras and superalgebras of vector fields, Uspekhi Mat. Nauk 37 (1982), no. 2(224), 233–234 (Russian). MR 650787
  • [Fu] D. B. Fuks, Cohomology of infinite-dimensional Lie algebras, Contemporary Soviet Mathematics, Consultants Bureau, New York, 1986. Translated from the Russian by A. B. Sosinskiĭ. MR 874337
  • [G] Howard Garland, Dedekind’s 𝜂-function and the cohomology of infinite dimensional Lie algebras, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), no. 7, 2493–2495. MR 0387361
  • [GL] Howard Garland and James Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), no. 1, 37–76. MR 0414645
  • [K] Bertram Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329–387. MR 0142696
  • [L] J. Lepowsky, Generalized Verma modules, loop space cohomology and MacDonald-type identities, Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 2, 169–234. MR 543216
  • [M] J. C. Moore, Algebre homologique et homologie espace classificants, Sem. H. Cartan, Expose 7, 1959/60.
  • [S] Jean-Pierre Serre, Groupes d’homotopie et classes de groupes abéliens, Ann. of Math. (2) 58 (1953), 258–294 (French). MR 0059548

Similar Articles

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

Retrieve articles in all journals with MSC: 17B56


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1198456-X
Keywords: Affine Lie algebra, adjoint representation, Lie algebra cohomology, spectral sequence
Article copyright: © Copyright 1994 American Mathematical Society