second cohomology of lie rings and the schur multiplier

نویسندگان

max horn

seiran zandi

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 theory

ناشر: university of isfahan

ISSN 2251-7650

دوره 3

شماره 2 2014

میزبانی شده توسط پلتفرم ابری doprax.com

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