Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Central extensions of current algebras


Author: Paul Zusmanovich
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
Erratum: Trans. Amer. Math. Soc. 362 (2010), 5601-5603.
MathSciNet review: 1069751
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] R. E. Block, On the Mills-Seligman axioms for Lie algebras of classical type, Trans. Amer. Math. Soc. 121 (1966), 378-392. MR 0188356 (32:5795)
  • [2] -, On the extensions of Lie algebras, Canad. J. Math. 20 (1968), 1439-1450. MR 0235001 (38:3313)
  • [3] -, Determination of the differentiability simple rings with a minimal ideal, Ann. of Math. 90 (1969), 433-459. MR 0251088 (40:4319)
  • [4] N. Bourbaki, Groupes et algèbres de Lie, Chapitres VII, VIII, Hermann, Paris, 1975. MR 0453824 (56:12077)
  • [5] P. Cartier, Homologie cyclique: rapport sur les travaux récents de Connes, Karoubi, Loday, Quillen..., Astérisque 121-122 (1985), 123-148. MR 768957 (86e:18012)
  • [6] A. S. Dzhumadil'daev, Central extensions of the Zassenhaus algebra and their irreducible representations, Math. USSR-Sb. 54 (1986), 457-474. MR 788083 (86j:17017)
  • [7] D. B. Fuchs, Cohomology of infinite-dimensional Lie algebras, Consultants Bureau, New York, 1986. MR 874337 (88b:17001)
  • [8] A. Haddi, Détermination des extensions centralees des algèbres de Kac-Moody, C. R. Acad. Sci. Paris 306 (1988), 691-694. MR 944412 (89i:17018)
  • [9] C. Kassel, Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra, J. Pure Appl. Algebra 34 (1984), 265-275. MR 772062 (86h:17013)
  • [10] M. I. Kuznetsov, The modular simple Lie algebras with a solvable maximal subalgebra, Math. USSR-Sb. 30 (1976), 68-76.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B56, 17B50

Retrieve articles in all journals with MSC: 17B56, 17B50


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1069751-2
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society