Second cohomology of Lie rings and the Schur multiplier

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ID: 97382
2014
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Abstract
We exhibit an explicit construction for the second cohomology group$H^2(L, A)$ for a Lie ring $L$ and a trivial $L$-module $A$.We show how the elements of $H^2(L, A)$ correspond one-to-one to theequivalence classes of central extensions of $L$ by $A$, where $A$now is considered as an abelian Lie ring. For a finite Liering $L$ we also show that $H^2(L, C^*) cong M(L)$, where $M(L)$ denotes theSchur multiplier of $L$. These results match precisely the analoguesituation in group theory.
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horn2014secondinternational Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Horn, Max;Zandi, Seiran;
Journal international journal of group theory
Year 2014
DOI
DOI not found
URL
http://www.theoryofgroups.ir/?_action=showPDF&article=3589&_ob=cf135f0fb1340cca48124481e4a34726&fileName=full_text.pdf.
Keywords
Technology mathematics nuclear and particle physics. atomic energy. radioactivity

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