scholarly journals Classification of 6D Leibniz algebras

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Ladislav Hlavatý
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Leibniz Algebras ◽  
Drinfel’D Double ◽  
Generalized Frame

Abstract Leibniz algebras ${\mathcal E}_n$ were introduced as an algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi 3D Lie algebras are classified here. Two types of algebras are obtained: 6D Lie algebras that can be considered an extension of the semi-Abelian 4D Drinfel’d double and unique extensions of non-Abelian Bianchi algebras. For all of the algebras explicit forms of generalized frame fields are given.

scholarly journals The algebraic structure of relativistic wave equations

1978 ◽  
Vol 20 (4) ◽  
pp. 446-486 ◽  
Author(s):  
A. Cant ◽  
C. A. Hurst
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Mass Spectra ◽  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave ◽  
Partial Classification ◽  
The Family ◽  
Image Position

The algebraic structure of relativistic wave equations of the formis considered. This leads to the problem of finding all Lie algebrasLwhich contain the Lorentz Lie algebraso(3, 1) and also contain a “four-vector” αμa such anLgives rise to a family of wave equations. The simplest possibility is the Bhabha equations whereL≅so(5). Some authors have claimed that this is theonlyone, but it is shown that there are many other possibilities still in accord with physical requirements. Known facts about representations, along with Dynkin's theory of the embeddings of Lie algebras, are used to obtain a partial classification of wave equations. The discrete transformationsC, P, Tare also discussed, along with reality properties. Finally, a simple example of a family of wave equations based onL=sp(12) is considered in detail. Theso(3, 1) content and mass spectra are given for the low order members of the family, and the problem of causality is briefly discussed.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

scholarly journals Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A)=3

2016 ◽  
Vol 110 ◽  
pp. 25-29 ◽  
Author(s):  
Hamid Darabi ◽  
Farshid Saeedi ◽  
Mehdi Eshrati
Keyword(s):  
Lie Algebras

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

Complete classification of pseudo H-type Lie algebras: I

2017 ◽  
Vol 190 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Kenro Furutani ◽  
Irina Markina
Keyword(s):  
Lie Algebras ◽  
Complete Classification

Classification of three-dimensional solvable p-adic Leibniz algebras

2010 ◽  
Vol 2 (3) ◽  
pp. 207-221 ◽  
Author(s):  
A. Kh. Khudoyberdiyev ◽  
T. K. Kurbanbaev ◽  
B. A. Omirov
Keyword(s):  
Three Dimensional ◽  
Leibniz Algebras

Classification of Filiform Leibniz Algebras in Low Dimensions

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov
Keyword(s):  
Low Dimensions ◽  
Leibniz Algebras

scholarly journals Algebraic Structure of the Lorentz and of the Poincaré Lie Algebras

2018 ◽  
Vol 41 (2) ◽  
pp. 305-346
Author(s):  
Pablo ALBERCA BJERREGAARD ◽  
Dolores MARTÍN BARQUERO ◽  
Cándido MARTÍN GONZÁLEZ ◽  
Daouda NDOYE
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure

scholarly journals On classification of (n+6)-dimensional nilpotent n-Lie algebras of class 2 with n≥4

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Jamshidi ◽  
Farshid Saeedi ◽  
Hamid Darabi
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Design Methodology ◽  
Central Element ◽  
Complete Understanding ◽  
Content Type ◽  
Low Dimension

PurposeThe purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.Design/methodology/approachBy dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.FindingsIn this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.Originality/valueThis classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

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