Lie triple system central extensions of Lie algebras

2010/10/08 by Revaz Kurdiani, Kurdiani, Revaz
Mathematics · #17A32 #17A40 #17B55 #17D99 #18G15 #18G55 19C09 #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.KT #math.RA #math.RT #msc:17A32 #msc:17A40 #msc:17B55 #msc:17D99 #msc:18G15 #msc:18G55 #msc:19C09

paper · pdf · doi:10.48550/arxiv.1010.1760

arxiv created 2010/10/08 · arxiv updated 2010/10/11

Abstract

Three kinds of universal central extension are considered for a perfect Lie algebra. More precisely, one can consider such a Lie algebra as a Lie triple system, or a Leibniz algebra and construct appropriate central extensions. We show that Lie triple system universal central extension is isomorphic either to Lie or Leibniz algebra universal central extension considered as a Lie triple system in appropriate way.

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