Central extensions of current algebras
HTML articles powered by AMS MathViewer
- by Paul Zusmanovich
- Trans. Amer. Math. Soc. 334 (1992), 143-152
- DOI: https://doi.org/10.1090/S0002-9947-1992-1069751-2
- PDF | Request permission
Erratum: Trans. Amer. Math. Soc. 362 (2010), 5601-5603.
Abstract:
The second cohomology group of Lie algebras of kind $L \otimes U$ with trivial coefficients is investigated, where $L$ admits a decomposition with one-dimensional root spaces and $U$ is an arbitrary associative commutative algebra with unit. This paper gives a unification of some recent results of C. Kassel and A. Haddi and provides a determination of central extensions of certain modular semisimple Lie algebras.References
- Richard E. Block, On the Mills-Seligman axioms for Lie algebras of classical type, Trans. Amer. Math. Soc. 121 (1966), 378–392. MR 188356, DOI 10.1090/S0002-9947-1966-0188356-3
- Richard E. Block, On the extensions of Lie algebras, Canadian J. Math. 20 (1968), 1439–1450. MR 235001, DOI 10.4153/CJM-1968-145-5
- Richard E. Block, Determination of the differentiably simple rings with a minimal ideal, Ann. of Math. (2) 90 (1969), 433–459. MR 251088, DOI 10.2307/1970745
- N. Bourbaki, Éléments de mathématique. Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1364, Hermann, Paris, 1975 (French). MR 0453824
- Pierre Cartier, Homologie cyclique: rapport sur des travaux récents de Connes, Karoubi, Loday, Quillen$\ldots$, Astérisque 121-122 (1985), 123–146 (French). Seminar Bourbaki, Vol. 1983/84. MR 768957
- A. S. Dzhumadil′daev, Central extensions of the Zassenhaus algebra and their irreducible representations, Mat. Sb. (N.S.) 126(168) (1985), no. 4, 473–489, 592 (Russian). MR 788083
- 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
- Aziz Haddi, Détermination des extensions centrales des algèbres de Kac-Moody, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 16, 691–694 (French, with English summary). MR 944412
- Christian Kassel, Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra, Proceedings of the Luminy conference on algebraic $K$-theory (Luminy, 1983), 1984, pp. 265–275. MR 772062, DOI 10.1016/0022-4049(84)90040-9 M. I. Kuznetsov, The modular simple Lie algebras with a solvable maximal subalgebra, Math. USSR-Sb. 30 (1976), 68-76.
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 334 (1992), 143-152
- MSC: Primary 17B56; Secondary 17B50
- DOI: https://doi.org/10.1090/S0002-9947-1992-1069751-2
- MathSciNet review: 1069751