Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef

Displaying similar documents to “Algorithmic computations of Lie algebras cohomologies”

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

Similarity:

We classify all complex $7$ - and $8$ -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex $9$ -dimensional dual mock-Lie algebras.

Local superderivations on Lie superalgebra $𝔮 (n)$

Haixian Chen, Ying Wang (2018)

Czechoslovak Mathematical Journal

Similarity:

Let $𝔮 (n)$ be a simple strange Lie superalgebra over the complex field $ℂ$ . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over $ℂ$ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but $𝔭 (n)$ is an exception....

$𝔤$ -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

Similarity:

A Lie version of Turaev’s $\bar{G}$ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a $𝔤$ -quasi-Frobenius Lie algebra for $𝔤$ a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra $(𝔮, β)$ together with a left $𝔤$ -module structure which acts on $𝔮$ via derivations and for which $β$ is $𝔤$ -invariant. Geometrically, $𝔤$ -quasi-Frobenius Lie algebras are the Lie algebra structures associated to...

The groups of automorphisms of the Witt $W_{n}$ and Virasoro Lie algebras

Vladimir V. Bavula (2016)

Czechoslovak Mathematical Journal

Similarity:

Let $L_{n} = K [x_{1}^{\pm 1}, ..., x_{n}^{\pm 1}]$ be a Laurent polynomial algebra over a field $K$ of characteristic zero, $W_{n} : = {Der}_{K} (L_{n})$ the Lie algebra of $K$ -derivations of the algebra $L_{n}$ , the so-called Witt Lie algebra, and let $Vir$ be the Virasoro Lie algebra which is a $1$ -dimensional central extension of the Witt Lie algebra. The Lie algebras $W_{n}$ and $Vir$ are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: ${Aut}_{Lie} (Vir) ≃ {Aut}_{Lie} (W_{1}) ≃ {\pm 1} ⋉ K^{*}$ , and give a short proof that ${Aut}_{Lie} (W_{n}) ≃ {Aut}_{K - alg} (L_{n}) ≃ {GL}_{n} (ℤ) ⋉ K^{* n}$ .

When unit groups of continuous inverse algebras are regular Lie groups

Helge Glöckner, Karl-Hermann Neeb (2012)

Studia Mathematica

Similarity:

It is a basic fact in infinite-dimensional Lie theory that the unit group $A^{\times}$ of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group $A^{\times}$ is regular in Milnor’s sense. Notably, $A^{\times}$ is regular if A is Mackey-complete and locally m-convex.

Regular orbital measures on Lie algebras

Alex Wright (2008)

Colloquium Mathematicae

Similarity:

Let H₀ be a regular element of an irreducible Lie algebra , and let $μ_{H ₀}$ be the orbital measure supported on $O_{H ₀}$ . We show that $μ ̂_{H ₀}^{k} \in L ² ()$ if and only if k > dim /(dim - rank ).

$\mathcal{L}$ -homomorphisms of Lie algebras

Aleksander A. Lashkhi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Si studiano gli omomorfismi reticolari ( $\mathcal{L}$ -omomorfismi) di algebre di Lie sopra anelli commutativi con unità. Le algebre di Lie sopra un campo e le $p$ -algebre di Lie non ammettono $\mathcal{L}$ -omomorfismi propri. Si assegnano condizioni necessarie e sufficienti affinchè un'algebra di Lie periodica o mista possieda un « $\mathcal{L}$ -omomorfismo su una catena di lunghezza $n$ .

Quantization of semisimple real Lie groups

Kenny De Commer (2024)

Archivum Mathematicum

Similarity:

We provide a novel construction of quantized universal enveloping $*$ -algebras of real semisimple Lie algebras, based on Letzter’s theory of quantum symmetric pairs. We show that these structures can be ‘integrated’, leading to a quantization of the group C $^{*}$ -algebra of an arbitrary semisimple algebraic real Lie group.

Quantized semisimple Lie groups

Rita Fioresi, Robert Yuncken (2024)

Archivum Mathematicum

Similarity:

The goal of this expository paper is to give a quick introduction to $q$ -deformations of semisimple Lie groups. We discuss principally the rank one examples of $𝒰_{q} ({𝔰𝔩}_{2})$ , $𝒪 ({SU}_{q} (2))$ , $𝒟 ({SL}_{q} (2, ℂ))$ and related algebras. We treat quantized enveloping algebras, representations of $𝒰_{q} ({𝔰𝔩}_{2})$ , generalities on Hopf algebras and quantum groups, $*$ -structures, quantized algebras of functions on $q$ -deformed compact semisimple groups, the Peter-Weyl theorem, $*$ -Hopf algebras associated to complex semisimple Lie groups and the Drinfeld...