second cohomology of lie rings and the schur multiplier
نویسندگان
چکیده
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.
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عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 3
شماره 2 2014
میزبانی شده توسط پلتفرم ابری doprax.com
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