Results 21 to 30 of about 277 (187)

Noncomplete affine structures on Lie algebras of maximal class

International Journal of Mathematics and Mathematical Sciences, 2002
Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent.
E. Remm, Michel Goze
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Group algebras and Lie nilpotence

Journal of Algebra, 2013
Let \(F\) be a field of characteristic zero or odd prime characteristic \(p\), \(G\) a group, \(FG\) the group algebra. The authors continue their research on the properties of symmetric and skew-symmetric elements of \(FG\) with respect to an algebra involution \(*\) induced by an involution on the group, communicated in a series of papers, recent ...
GIAMBRUNO, Antonino, Polcino Milies, C, Sehgal, S.   +2 more
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On Marginal Automorphisms of Free Nilpotent Lie Algebras

Journal of Mathematics, 2020
Let L be the free nilpotent Lie algebra of finite rank over a field of characteristic zero. We define the concepts of marginal ideals and marginal automorphisms of L, and we give some results on marginal automorphisms.
Özge Öztekin
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Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

Complex Manifolds, 2017
Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t.
Yamada Takumi
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Further results on q-Lie groups, q-Lie algebras and q-homogeneous spaces

Special Matrices, 2021
We introduce most of the concepts for q-Lie algebras in a way independent of the base field K. Again it turns out that we can keep the same Lie algebra with a small modification.
Ernst Thomas
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k-step nilpotent Lie algebras [PDF]

Georgian Mathematical Journal, 2015
Abstract The classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy.
Goze, Michel, Remm, Elisabeth
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On Equality of Certain Derivations of Lie Algebras

Discussiones Mathematicae - General Algebra and Applications, 2019
Let L be a Lie algebra. A derivation α of L is a commuting derivation (central derivation), if α (x) ∈ CL (x) (α (x) ∈ Z (L)) for each x ∈ L. We denote the set of all commuting derivations (central derivations) by 𝒟 (L) (Derz (L)).
Amiri Azita, Saeedi Farshid, Alemi Mohammad Reza   +2 more
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$7$-dimensional nilpotent Lie algebras [PDF]

Transactions of the American Mathematical Society, 1993
All 7-dimensional complex nilpotent Lie algebras are determined. The algebras are listed in tables, categorized by the dimensions of the terms in the upper central series. In each such category, the algebras are listed as decomposable or indecomposable and for those algebras in the latter, distinguishing features are provided.
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CAPABILITY OF LOW-DIMENSIONAL NILPOTENT 3-LIE ALGEBRAS [PDF]

Journal of Algebraic Systems
In this paper, we characterize the capability of nilpotent n- Lie algebras of dimensionat most n + 3 over an arbitrary field when n > 2$ and the capability of 7 -dimensional nilpotent 3 -Lie algebras over field $\mathcal {K} $ with $char \mathcal {K}\ ne
Hamid Darabi
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Nilpotent symmetries as a mechanism for Grand Unification

Journal of High Energy Physics, 2021
In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential.
Lars Andersson, András László, Błażej Ruba   +2 more
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