Lie algebra expansions and actions for non-relativistic gravity
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DOI: 10.1007/jhep08(2019)048
Abstract: Abstract We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method… read more here.
Keywords: relativistic gravity; lie algebra; algebra expansions; actions non ... See more keywords
On Characterizing Nilpotent Lie Algebra by Their Multiplier, $$ s(L)=6, 7 $$
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DOI: 10.1007/s00025-022-01616-5
Abstract: Let L be an n-dimensional non-abelian nilpotent Lie algebra and s(L) = 1 2 (n − 1)(n − 2) + 1 − dimM(L) where M(L) is the Schur multiplier of a Lie algebra L. The… read more here.
Keywords: lie; lie algebra; nilpotent lie; algebra multiplier ... See more keywords
Matsushima–Lichnerowicz type theorems of Lie algebra of automorphisms of generalized Kähler manifolds of symplectic type
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DOI: 10.1007/s00208-021-02299-z
Abstract: In Kahler geometry, Fujiki--Donaldson show that the scalar curvature arises as the moment map for Hamiltonian diffeomorphisms. In generalized Kahler geometry, one does not have good notions of Levi-Civita connection and curvature, however there still… read more here.
Keywords: kahler; algebra automorphisms; geometry; type ... See more keywords
The R-Matrix Presentation for the Yangian of a Simple Lie Algebra
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DOI: 10.1007/s00220-018-3227-4
Abstract: Starting from a finite-dimensional representation of the Yangian $${Y (\mathfrak{g})}$$Y(g) for a simple Lie algebra $$ \mathfrak{g}$$g in Drinfeld’s original presentation, we construct a Hopf algebra $${{X}_\mathcal{I}(\mathfrak{g})}$$XI(g), called the extended Yangian, whose defining relations are… read more here.
Keywords: algebra; lie; matrix; simple lie ... See more keywords
Spectral Characters of a Class of Integrable Representations of Toroidal Lie Algebras
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DOI: 10.1007/s10468-018-9816-2
Abstract: In this paper we study the subcategory of finite-length objects of the category of positive level integrable representations of a toroidal Lie algebra. The main goal is to characterize the blocks of the category. In… read more here.
Keywords: characters class; integrable representations; toroidal lie; lie algebra ... See more keywords
Lie algebra of coupled higher-dimensional forced Burgers’ equation
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DOI: 10.1007/s13370-021-00926-1
Abstract: Symmetry analysis of coupled higher-dimensional forced Burgers’ equation is investigated for various cases. The Lie algebra for the various cases of forcing terms is investigated. Interestingly, for a linear forcing term, the symmetry analysis leads… read more here.
Keywords: burgers equation; dimensional forced; forced burgers; coupled higher ... See more keywords
Finite and infinite dimensional Lie group structures on Riordan groups
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DOI: 10.1016/j.aim.2017.08.033
Abstract: Abstract We introduce a Frechet Lie group structure on the Riordan group. We give a description of the corresponding Lie algebra as a vector space of infinite lower triangular matrices. We describe a natural linear… read more here.
Keywords: lie group; lie; group; groups finite ... See more keywords
On the smoothness of some quotients of Banach-Lie groups
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DOI: 10.1016/j.difgeo.2019.101556
Abstract: Abstract Quotients of Banach-Lie groups are regarded as topological groups with Lie algebra in the sense of Hofmann-Morris on the one hand, and as Q-groups in the sense of Barre-Plaisant on the other hand. For… read more here.
Keywords: lie groups; lie algebra; smoothness quotients; banach lie ... See more keywords
Cohomology and Deformations of $n$-Lie algebra morphisms
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DOI: 10.1016/j.geomphys.2018.05.010
Abstract: Abstract The study of n -Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define… read more here.
Keywords: cohomology deformations; lie algebra; algebra morphisms; deformations lie ... See more keywords
Multi derivation Maurer-Cartan algebras and sh-Lie-Rinehart algebras
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DOI: 10.1016/j.jalgebra.2016.10.008
Abstract: Abstract We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer–Cartan algebra—the familiar differential graded algebra of alternating forms on g with values in the ground field, endowed with… read more here.
Keywords: algebra; lie rinehart; rinehart algebras; lie algebra ... See more keywords
Symplectic, product and complex structures on 3-Lie algebras
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DOI: 10.1016/j.jalgebra.2018.05.005
Abstract: Abstract In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to… read more here.
Keywords: lie algebras; lie algebra; product; structure ... See more keywords