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 作者：J.M. Escobar , J. Núñez , P. Pérez-Fernández 来源：[J].Journal of Nonlinear Mathematical Physics(IF 0.569), 2018, Vol.25 (3), pp.358-374Taylor & Francis 摘要：In this paper, we deal with contractions of Lie algebras. We use two invariant functions of Lie algebras as a tool, named ψ and ϕ function, respectively, which have a great application in Physics due to their remarkable properties. We focus the study of these functions in t...
 作者：Alice Fialowski , Marc de Montigny 来源：[J].Symmetry, Integrability and Geometry: Methods and Applications(IF 1.243), 2006, Vol.2, pp.048DOAJ 摘要：In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras...
 作者：E. N. Poroshenko 来源：[J].Siberian Mathematical Journal(IF 0.285), 2017, Vol.58 (2), pp.296-304Springer 摘要：We study universal theories of partially commutative Lie algebras, partially commutative metabelian Lie algebras, and partially commutative metabelian groups such that their defining graphs are trees with countably many vertices. Also we find universal equivalence criteria for ea...
 作者：Taras V. Skrypnyk 来源：[J].Symmetry, Integrability and Geometry: Methods and Applications(IF 1.243), 2006, Vol.2, pp.043DOAJ 摘要：We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in "principal" gradation and admit Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classica...
 作者：Taras V. Skrypnyk 来源：[J].Symmetry, Integrability and Geometry: Methods and Applications(IF 1.243), 2006, Vol.2DOAJ 摘要：We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in "principal" gradation and admit Kostant-Adler-Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classica...
 作者：E. N. Poroshenko 来源：[J].Algebra and Logic(IF 0.493), 2017, Vol.56 (2), pp.133-148Springer 摘要：We study universal theories of partially commutative Lie algebras whose defining graphs are cycles and trees. Within each of the two above-mentioned classes of partially commutative Lie algebras, necessary and sufficient conditions for the coincidence of universal theories are sp...
 作者：Antonio J. Calderón Martín 来源：[J].Proceedings Mathematical Sciences(IF 0.191), 2008, Vol.118 (3), pp.351-356Springer 摘要：Abstract(#br)We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras L is of the form L = $$\mathcal{U}$$ + Σ j I j with $$\mathcal{U}$$ a subspace of the abelian Lie algebra H and any I j a well descr...
 作者：Haisheng Li , Shaobin Tan , Qing Wang 来源：[J].Advances in Mathematics(IF 1.373), 2020, Vol.363Elsevier 摘要：Abstract(#br)In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the covariant algebras of the affine ...
 作者：Vincent Knibbeler , Sara Lombardo , Jan A. Sanders 来源：[J].Foundations of Computational Mathematics(IF 1.918), 2017, Vol.17 (4), pp.987-1035Springer 摘要：The paper presents the complete classification of Automorphic Lie Algebras based on $${{\mathfrak {sl}}}_{n}(\mathbb {C})$$ , where the symmetry group G is finite and acts on $${{\mathfrak {sl}}}_n(\mathbb {C})$$ by inner automorphisms, $${{\mathfrak {sl}}}_n(\mathbb {C})$$ has n...
 作者：Kenro Furutani , Irina Markina 来源：[J].Geometriae Dedicata(IF 0.465), 2017, Vol.190 (1), pp.23-51Springer 摘要：Let $${\mathscr {N}}$$ be a 2-step nilpotent Lie algebra endowed with a non-degenerate scalar product $$\langle .\,,.\rangle$$ , and let $${\mathscr {N}}=V\oplus _{\perp }Z$$ , where Z is the centre of the Lie algebra and V its orthogonal complement. We study classification of t...