Lie algebras
Elementary Lie Algebras and Lie A Algebras
... finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is ...semisimple Lie ...
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Schur Multipliers of Nilpotent Lie Algebras.
... Eq. 4.1 indicates that a given value for t(L) will result in two possible choices for n. For instance if t(L) = 3, then both n = 3 and n = 4 satisfy Eq. 4.1. From the results collected in Table 3.1, we do not see that to ...
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Two Generator Subalgebras Of Lie Algebras
... finite-dimensional Lie algebras over infinite fields of characteristic greater than ...supersolvable Lie algebras, and the property of ...
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C Supplemented Subalgebras of Lie Algebras
... The concept of a c-supplemented subgroup of a finite group was introduced by Ballester-Bolinches, Wang and Xiuyun in [2] and has since been studied by a number of authors. The purpose of this paper is study the ...
9
The ideal and subideal structure of lie algebras
... in Lie algebras along the same line as ideals in an associative rings,and investigate some of their ...of Lie algebras with certain finiteness conditions on subideals, using the notion of ...
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On Characterizing Nilpotent Lie algebras by their Multipliers
... By Theorem 4, we know that c 2 + c ≤ 2t where c = dimL 2 and t= t(L). If t =21 then c 2 + c ≤ 42 which implies that c ≤ 6 therefore c = 0, 1, 2, 3, 4,5 or 6 but by proposition 0 (i.e. t ≤ ½n(n-1)) and since n= c+2 for ...
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Frattini theory for \(N\)-Lie algebras
... 𝑅(𝐴) is the vector space generated by all right multiplications of 𝐴. In [7 Theorem 2.2] we proved for 𝐴 an 𝑛-Lie algebra, 𝐴 is nilpotent if and only if 𝜙(𝐴) = 𝐴 2 which coresponds to Barnes’ and Chao’s work. In ...
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Automorphic equivalence of the representations of Lie algebras
... all Lie algebras with projection- ...are Lie algebras with all operations and axioms of Lie algebras and with one additional unary operation: pro- jection p, which fulfills two ...
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Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities
... affine Lie algebras and ultimately led to the discovery of new combinatorial identities (see for example [3] and [7]) and new algebraic structures such as vertex (operator) algebras (see for example ...
104
On nilpotent filiform Lie algebras of dimension eight
... filiform Lie algebras g of dimension 8 and that of the set of nilpotent filiform Lie algebras whose group of automorphisms consists of unipo- tent automorphisms, in the variety of filiform ...
16
On action of outer derivations on nilpotent ideals of Lie algebras
... a Lie algebra L over a field F under an outer derivation lies in a nilpotent ideal provided that n < p− 1, where p = ...of Lie algebras over fields of positive ...
9
Casimirs and Lax Operators from the Structure of Lie algebras
... The defining property of a Casimir functions is provided. A necessary requirement of them is identified as well as a theorem on finding further examples. This information is used to find the Casimir functions for some 3 ...
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Classical Banach Lie algebras and Banach Lie groups of operators in Hilbert space
... The methods used have been suggested hy the theories of finite dimensional semi-simple real and complex Lie algebras, and of associative Banach algebras of linear operators.. The results[r] ...
190
Nonstandard hulls of locally exponential Lie algebras
... dimensional Lie algebras in order to generalize a theorem of Pestov on the en- largeability of Banach-Lie algebras, yielding a partial answer to a question of Neeb from ...
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Subalgebras of free nilpotent and polynilpotent lie algebras
... soluble Lie algebras, which are finitely-generated as subalgebras» -be next section deals w ith the sam e problem in the context of fre e polyni 1 potent Lie algebras* In sections three and ...
165
Reduction groups and automorphic Lie algebras
... semi-simple Lie algebras, discuss the structure of automorphisms groups of algebras over a ring of rational functions and define automorphic Lie ...
22
Zassenhaus varieties of general linear Lie algebras
... 3.3. As mentioned in the introduction, our proof of the main theorem will rely on the following proposition communicated to us by S. Skryabin. We were unable to trace this result in the literature. Although it resembles ...
19
Classification of Nilpotent Lie Algebras with Small Breadth.
... simple Lie algebras due to Killing and ...of Lie algebras. In particular, the vast number of nilpotent Lie algebras has made the classification problem formidable for this ...
70
On nilpotent Lie algebras of derivations of fraction fields
... the Lie algebra of vector fields on R n with formal power series ...Such Lie algebras with polynomial, formal power series, or analytical coefficients were studied by many ...
13
Lie algebras of derivations with large abelian ideals
... such Lie algebras is ...the Lie algebra F L over the field F can be isomorphically embedded into the general affine Lie algebra aff m (F ...
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