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Kac-Moody-Malcev and super-Kac-Moody-Malcev algebras. (English) Zbl 0789.17031

Myung, Hyo Chul (ed.), Proceedings of the fifth international conference on hadronic mechanics and nonpotential interactions, held at the University of Northern Iowa, Cedar Falls, Iowa, USA, August 13-17, 1990. Part 1: Mathematics. New York: Nova Science Publishers. 259-265 (1992).
Given a Malcev algebra \(M\), the author considers analogous constructions to the realizations of non-twisted affine Lie algebras [see the book by V. G. Kac, Infinite dimensional Lie algebras, 2nd ed. (1985; Zbl 0574.17010) (3rd ed. 1990; Zbl 0716.17022)]. Hence, the loop algebra \(M(t) = M \otimes {\mathbb{C}}[t,t^{-1}]\) and its one-dimensional central extensions are considered. Moreover, by taking also the Grassmann algebra in one generator \({\mathbb{C}}[\theta] = {\mathbb{C}}1+{\mathbb{C}}\theta\) with \(\theta^ 2 = 0\), the author also considers the superalgebra \(M(t) \otimes {\mathbb{C}}[\theta]\) and its central extensions. The case in which \(M\) is the non-Lie simple Malcev algebra of dimension 7 is given special attention.
For the entire collection see [Zbl 0773.00026].

MSC:

17D10 Mal’tsev rings and algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17A70 Superalgebras
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References:

[1] Coquereaux, R.; Frappat, L.; Ragoucy, E.; Sorba, P.: Preprintlapp-TH-246/89, CPT-89/PE-2269. Lapp-th-246/89, cpt-89/pe-2269 (May 1989)
[2] Osipov, E. P.: Lett. math. Phys.. 18, 35 (1989)
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