Journal ArticleDOI
On covers of lie algebras
Peggy Batten,Ernest Stitzinger +1 more
TLDR
For finite dimensional Lie algebras, covers are isomorphic as mentioned in this paper, and it is shown that covers need not be isomorphic to find all the extensions of a finite group.Abstract:
In dealing with the central extensions of a finite group G one finds that although covers need not be isomorphic, for each such H there exists a cover for which H is a. homomorphic image [1]. For finite dimensional Lie algebras, covers are isomorphic. We shall show that the second property also holds for Lie algebras. Thus to find all such extensions one needs to compute the cover and consider ideals contained in the multiplier (kernel of the homomorphism). Several examples are constructed. Our Lie algebras are taken over a field.read more
Citations
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Journal ArticleDOI
On characterizing nilpotent lie algebras by their multipliers
TL;DR: In this article, the authors obtained similar results for Lie algebras with order multipliers for groups of order pj whose multiplier has order, and for groups with order multiplier.
Journal ArticleDOI
Some Properties of the Schur Multiplier and Covers of Lie Algebras
TL;DR: In this paper, the structure of all covers of Lie algebras that their Schur multipliers are finite-dimensional is given, which generalizes the work of Batten and Stitzinger (1996).
Journal ArticleDOI
On characterizing nilpotent lie algebras by their multiplierst(L) = 3,4,5,6
Peter Hardy,Emest Stitzinger +1 more
TL;DR: In this paper, the same authors extended the results to t(L) = 3,4,5,6,7 and 8, using a different method, and showed that the multipliers have dimension ½n(n-1)-t(L).
Journal ArticleDOI
A Note on the Schur Multiplier of a Nilpotent Lie Algebra
TL;DR: For a nilpotent Lie algebra L of dimension n and dim(L 2 ) = m ≥ 1, the upper bound of the Schur multiplier of L was shown in this paper.
Journal ArticleDOI
Some criteria for detecting capable Lie algebras
TL;DR: In this paper, Niroom and Niroom et al. classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one.
References
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Book
The Schur multiplier
TL;DR: In this article, a large amount of research has been devoted to the study of various properties of the second cohomology group H 2 (G,C*), also known as the Schur multiplier of a group G. The present book ties together various threads of the development, and conveys a comprehensive picture of the current state of the subject.
Journal ArticleDOI
On Cancellation in Groups
TL;DR: In this article, Cancellation in groups is studied in the context of group cancellation in groups, and the authors propose a method to cancel groups in groups in the setting of groups.