Results 11 to 20 of about 277 (187)
On maximality of some solvable and locally nilpotent subalgebras of the Lie algebra $W_n(K)$
Researches in Mathematics, 2023 Let $K$ be an algebraically closed field of characteristic zero, $P_n=K[x_1,\ldots ,x_n]$ the polynomial ring, and $W_n(K)$ the Lie algebra of all $K$-derivations on $P_n$.
D.I. Efimov, M.S. Sydorov, K.Ya. Sysak
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Post-Lie algebra structures for nilpotent Lie algebras [PDF]
International Journal of Algebra and Computation, 2018 We study post-Lie algebra structures on [Formula: see text] for nilpotent Lie algebras. First, we show that if [Formula: see text] is nilpotent such that [Formula: see text], then also [Formula: see text] must be nilpotent, of bounded class. For post-Lie algebra structures [Formula: see text] on pairs of [Formula: see text]-step nilpotent Lie algebras
Dietrich Burde +2 more
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Computing the index of Lie algebras; pp. 265–271 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 The aim of this paper is to compute and discuss the index of Lie algebras. We consider the n-dimensional Lie algebras for n lt; 5 and the case of filiform Lie algebras which form a special class of nilpotent Lie algebras.
Hadjer Adimi, Abdenacer Makhlouf
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On Properties of the (2n+1)-Dimensional Heisenberg Lie Algebra
JTAM (Jurnal Teori dan Aplikasi Matematika), 2020 In the present paper, we study some properties of the Heisenberg Lie algebra of dimension . The main purpose of this research is to construct a real Frobenius Lie algebra from the Heisenberg Lie algebra of dimension .
Edi Kurniadi
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Axioms, 2023 In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation.
Tatyana V. Redkina +2 more
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On the derivations of cyclic Leibniz algebras
Karpatsʹkì Matematičnì Publìkacìï, 2022 Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear
M.M. Semko, L.V. Skaskiv, O.A. Yarovaya
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Some Upper Bounds for the Dimension of the c-Nilpotent Multiplier of a Pair of Lie Algebras
Discussiones Mathematicae - General Algebra and Applications, 2020 The notion of the Schur multiplier of a Lie algebra L was introduced by Batten in 1996. Recently, the first author introduced the concept of the cnilpotent multiplier of a pair of Lie algebras and gave some exact sequences for the c-nilpotent multiplier ...
Arabyani Homayoon +2 more
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LIE ALGEBRA PREDERIVATIONS AND STRONGLY NILPOTENT LIE ALGEBRAS [PDF]
Communications in Algebra, 2002 We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.
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Applying Group Theory Philosophy to Leibniz Algebras: Some New Developments [PDF]
Advances in Group Theory and Applications, 2020 This survey is an attempt of describing of main contours of a recently developing general theory of Leibniz Algebras. This theory based on the employing of methods and approaches which are proved to be exceedingly effective in infinite group theory.
Leonid A. Kurdachenko +2 more
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Hodge decomposition of string topology
Forum of Mathematics, Sigma, 2021 Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free ...
Yuri Berest +2 more
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