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

λ-Mappings Between Representation Rings of Lie Algebras

1983 ◽  
Vol 35 (5) ◽  
pp. 898-960 ◽  
Author(s):  
R. V. Moody ◽  
A. Pianzola
Keyword(s):  
Root System ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Complete Classification ◽  
Representation Rings ◽  
Mathematical Formalization ◽  
Intuitive Idea ◽  
Image Position

In [10] Patera and Sharp conceived a new relation, subjoining, between semisimple Lie algebras. Our objective in this paper is twofold. Firstly, to lay down a mathematical formalization of this concept for arbitrary Lie algebras. Secondly, to give a complete classification of all maximal subjoinings between Lie algebras of the same rank, of which many examples were already known to the above authors.The notion of subjoining is a generalization of the subalgebra relation between Lie algebras. To give an intuitive idea of what is involved we take a simple example. Suppose is a complex simple Lie algebra of type B2. Let be a Cartan subalgebra of and Δ the corresponding root system. We have the standard root diagramInside B2 there lies the subalgebra A1 × A1 which can be identified with the sum of and the root spaces corresponding to the long roots of B2.

scholarly journals A complete classification of four-dimensional paraKähler Lie algebras

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Giovanni Calvaruso
Keyword(s):  
Lie Algebras ◽  
Riemannian Metric ◽  
Complete Classification

AbstractWe consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.

Cartan Subalgebras of Zassenhaus Algebras

1975 ◽  
Vol 27 (5) ◽  
pp. 1011-1021 ◽  
Author(s):  
Gordon Brown
Keyword(s):  
Lie Algebras ◽  
Characteristic Zero ◽  
Complete Classification ◽  
The Other ◽  
Closed Field ◽  
Finite Characteristic ◽  
Simple Lie Algebras ◽  
Finite Dimensional ◽  
Cartan Subalgebras

Cartan subalgebras play a very important role in the classification of the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic zero. It is well-known [5, 273] that any two Cartan subalgebras of such an algebra are conjugate, i.e. images of one another under some automorphism of the algebra. On the other hand, there exist finitedimensional simple Lie algebras over fields of finite characteristic p possessing non-conjugate Cartan subalgebras [2; 3; 4]. The simple Lie algebras discovered by Zassenhaus [6] also possess non-conjugate Cartan subalgebras, and we shall give a complete classification of Cartan subalgebras of these algebras in this paper.

scholarly journals Airy Structures for Semisimple Lie Algebras

2021 ◽  
Author(s):  
Leszek Hadasz ◽  
Błażej Ruba
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Complete Classification ◽  
Semiclassical Analysis ◽  
Simple Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Gauge Transformations ◽  
Finite Dimensional ◽  
Countably Infinite

AbstractWe give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also over $${\mathbb {R}}$$ R , up to isomorphisms and gauge transformations. The result is that the only algebras of this type which admit any Airy structures are $$\mathfrak {sl}_2$$ sl 2 , $$\mathfrak {sp}_4$$ sp 4 and $$\mathfrak {sp}_{10}$$ sp 10 . Among these, each admits exactly two non-equivalent Airy structures. Our methods apply directly also to semisimple Lie algebras. In this case it turns out that the number of non-equivalent Airy structures is countably infinite. We have derived a number of interesting properties of these Airy structures and constructed many examples. Techniques used to derive our results may be described, broadly speaking, as an application of representation theory in semiclassical analysis.

BUNDLES OF LIE ALGEBRAS

2013 ◽  
Vol 10 (09) ◽  
pp. 1350045 ◽  
Author(s):  
BÉCHIR DALI
Keyword(s):  
Lie Algebras ◽  
Complete Classification

In this paper, a complete classification of completely irreducible closed linear bundles of Lie algebras is given. We also apply the so-called "Raïs formula" to compute the index of each of the Lie bundles of square matrices.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

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