%0 Journal Article
%T Second cohomology of Lie rings and the Schur multiplier
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Horn, Max
%A Zandi, Seiran
%D 2014
%\ 06/01/2014
%V 3
%N 2
%P 9-20
%! Second cohomology of Lie rings and the Schur multiplier
%K Lie rings
%K Schur multiplier of Lie rings
%K central extension
%K second cohomology group of Lie rings
%R 10.22108/ijgt.2014.3589
%X 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 the equivalence classes of central extensions of $L$ by $A$, where $A$ now is considered as an abelian Lie ring. For a finite Lie ring $L$ we also show that $H^2(L, C^*) \cong M(L)$, where $M(L)$ denotes the Schur multiplier of $L$. These results match precisely the analogue situation in group theory.
%U https://ijgt.ui.ac.ir/article_3589_cf135f0fb1340cca48124481e4a34726.pdf