Abstract
In this article the universal central extensions of Lie superalgebras related to simple complex Lie superalgebras having nondegenerate Killing form are considered.
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REFERENCES
Bloch S., “The dilogarithm and extensions of Lie algebras, algebraic k-theory,” Evanston 1980, Springer Lecture Notes in Math., No. 854, 1–23 (1981).
Garland H., “The arithmetic theory of loop groups,” I. H. E. S., 52, 5–136 (1980).
Kac V. G., “Lie superalgebras,” Adv. Math., 26, No. 1, 8–96 (1977).
Kassel C., “Kähler differentials and covering of complex simple Lie algebras extended over a commutative algebra,” J. Pure and Appl. Algebra, 34, 265–275 (1984).
Kassel C. and Loday J.-L., “Extensions centrales d'algébres de Lie,” Ann. Inst. Fourier, 32,119–142 (1982).
Mikhalev A. V. and Pinchuk I. A., “Universal central extensions of t e matrix Lie superalgebras sl(m,n,A ),” Int. Conf. in H. K.U., AMS, 111–125 (2000).
Mikhalev A.V. and Pinchuk I. A., “Universal central extension of a particular Lie superalgebra with nonde-generate Killing form,” Universal Algebra and Its Applications, Volgograd, 201–221 (2000).
Pais A.,“On spinors in n dimensions,” J. Math. Phys., 3,1135 (1962).
Scheunert M., The Theory of Lie Superalgebras, Lecture Notes in Mat., No. 716 (1979).
Scheunert M., Nahm N., and Prittenberg V., “Classification of all simple graded Lie algebras whose Lie algebra is reductive. II. Construction of the exceptional algebras,” J. Math. Phys., 17, 1640 (1976).
Fuchs D.B., Cohomologies of In nite Dimensional Lie Algebras[Russian translation ], Nauka, Moscow (1982).
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Mikhalev, A.V., Pinchuk, I.A. Universal Central Extensions of Lie Superalgebras. Journal of Mathematical Sciences 114, 1547–1560 (2003). https://doi.org/10.1023/A:1022265215037
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DOI: https://doi.org/10.1023/A:1022265215037