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- Title
SOME PROPERTIES ON THE SCHUR MULTIPLIER OF A PAIR OF LIE ALGEBRAS.
- Authors
RISMANCHIAN, MOHAMMAD REZA; ARASKHAN, MEHDI; Sehgal, S.
- Abstract
The aim of this paper is to introduce the concept of the Schur multiplier ${\mathcal M}(L, N)$ of a pair of Lie algebras and to obtain some inequalities for the dimension of ${\mathcal M}(L, N)$. Also, we consider some of the features of central extension of an arbitrary Lie algebra. Moreover, we present a necessary and sufficient condition in which the Schur multiplier of a pair of Lie algebras can be embedded into the Schur multiplier of their factor Lie algebras.
- Subjects
LIE algebras; SCHUR multiplier; MATHEMATICAL inequalities; EMBEDDINGS (Mathematics); MULTIPLIERS (Mathematical analysis); MATHEMATICAL analysis; FACTOR analysis
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 1, p1250011-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498811005348