Some criteria for detecting capable Lie algebras
TLDR
In this paper, Niroom and Niroom et al. classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one.About:
This article is published in Journal of Algebra.The article was published on 2013-06-15 and is currently open access. It has received 60 citations till now. The article focuses on the topics: Nilpotent Lie algebra & Lie conformal algebra.read more
Citations
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Capability and Schur multiplier of a pair of Lie algebras
TL;DR: In this article, the exact structure of all pairs of capable Lie algebras in the class of abelian and Heisenberg ones is characterized. And the exact sequences on the Schur multiplier and exterior product of Lie algesbras are given.
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Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field
TL;DR: In this paper, the authors classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field, and the explicit structure of such Lie algesas of class 3 is given.
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On dimension of Schur multiplier of nilpotent Lie algebras II
TL;DR: For non-abelian nilpotent Lie algebras with dimension n, the authors showed that s(L) = 3 is a sufficient condition that L ≤ H(1) ⊕ F(n − 3).
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The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras
Peyman Niroomand,Farangis Johari +1 more
TL;DR: In this paper, the tensor square and the Schur multiplier of some nilpotent Lie algebras of class two have been studied and shown to be the same as in this paper.
References
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Book
An Introduction to Homological Algebra
TL;DR: An Introduction to Homological Algebra as discussed by the authors discusses the origins of algebraic topology and presents the study of homological algebra as a two-stage affair: first, one must learn the language of Ext and Tor and what it describes.
Journal ArticleDOI
Van Kampen theorems for diagrams of spaces
Ronald Brown,Jean-Louis Loday +1 more
TL;DR: In this article, a triad tensor product of two relative homotopy groups, each acting on the other via ;r,C is defined for a pair of groups M, N each of which acts on each other.
Book
The Structure of Groups of Prime Power Order
C. R. Leedham-Green,S. McKay +1 more
TL;DR: The proof of Conjecture A as mentioned in this paper shows that finite p-groups acting uniserially can be constructed in polynomial time, and the structure of finite P-groups can be found in Section 2.1.
Book
Groups of Prime Power Order 4
Yakov Berkovich,Zvonimir Janko +1 more
TL;DR: The fifth volume of a comprehensive and elementary treatment of finite p-group theory is as discussed by the authors, which includes many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.