Triple automorphisms of simple Lie algebras

Deng Yin Wang; Xiaoxiang Yu

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Displaying similar documents to “Triple automorphisms of simple Lie algebras”

The contact system on the $(m, ℓ)$ -jet spaces

J. Muñoz, F. J. Muriel, Josemar Rodríguez (2001)

Archivum Mathematicum

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This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system $Ω (M_{m}^{ℓ})$ on the space of $(m, ℓ)$ -velocities of a smooth manifold $M$ . Here we show that the characteristic system of $Ω (M_{m}^{ℓ})$ agrees with the Lie algebra of $Aut (ℝ_{m}^{ℓ})$ , the structure group of the principal fibre bundle ${\overset{ˇ}{M}}_{m}^{ℓ} ⟶ J_{m}^{ℓ} (M)$ , hence it is projectable to an irreducible contact system on the space of $(m, ℓ)$ -jets ( $= ℓ$ -th order contact elements of dimension $m$ ) of $M$ . Furthermore, we translate to the language of Weil bundles the structure...

The Wells map for abelian extensions of 3-Lie algebras

Youjun Tan, Senrong Xu (2019)

Czechoslovak Mathematical Journal

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The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions $0 \to A ↪ L \overset{π}{\to} B \to 0$ of 3-Lie algebras to obtain obstruction classes in $H^{1} (B, A)$ for a pair of automorphisms in $Aut (A) \times Aut (B)$ to be inducible from an automorphism of $L$ . Application to free nilpotent 3-Lie algebras is discussed.

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

Vladimir V. Bavula (2016)

Czechoslovak Mathematical Journal

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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 ${Aut}_{Lie} (W_{n}) ≃ {Aut}_{K - alg} (L_{n}) ≃ {GL}_{n} (ℤ) ⋉ K^{* n}$ .

Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra

Xing Wang, Daowei Lu, Ding-Guo Wang (2024)

Czechoslovak Mathematical Journal

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We study certain subgroups of the Hopf group-coalgebra automorphism group of Radford’s $π$ -biproduct. Firstly, we discuss the endomorphism monoid ${End}_{π -Hopf} (A \times H, p)$ and the automorphism group ${Aut}_{π -Hopf} (A \times H, p)$ of Radford’s $π$ -biproduct $A \times H = {A \times H_{α}}_{α \in π}$ , and prove that the automorphism has a factorization closely related to the factors $A$ and $H = {H_{α}}_{α \in π}$ . What’s more interesting is that a pair of maps $(F_{L}, F_{R})$ can be used to describe a family of mappings $F = {F_{α}}_{α \in π}$ . Secondly, we consider the relationship between the automorphism group ${Aut}_{π -Hopf} (A \times H, p)$ and the automorphism group...

Tight bounds for the dihedral angle sums of a pyramid

Sergey Korotov, Lars Fredrik Lund, Jon Eivind Vatne (2023)

Applications of Mathematics

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We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval $(3 π, 5 π)$ . Moreover, for any number in $(3 π, 5 π)$ there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound $4 π$ is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation...

Automorphisms of central extensions of type I von Neumann algebras

Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2011)

Studia Mathematica

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Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as $T = T_{a} \circ T_{ϕ}$ , where $T_{a} (x) = a x a^{- 1}$ is an inner automorphism implemented by an element a ∈ E(M), and $T_{ϕ}$ is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type $I_{\infty}$ then every band preserving...

Displaying similar documents to “Triple automorphisms of simple Lie algebras”

The contact system on the ( m , ℓ ) -jet spaces

The Wells map for abelian extensions of 3-Lie algebras

The groups of automorphisms of the Witt W n and Virasoro Lie algebras

Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra

Tight bounds for the dihedral angle sums of a pyramid

Automorphisms of central extensions of type I von Neumann algebras

The contact system on the $(m, ℓ)$ -jet spaces

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