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 M ˇ 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 → A ↪ L → π B → 0 of 3-Lie algebras to obtain obstruction classes in H 1 ( B , A ) for a pair of automorphisms in Aut ( A ) × 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 ± 1 , ... , x n ± 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 ) ≃ { ± 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 × H , p ) and the automorphism group Aut π -Hopf ( A × H , p ) of Radford’s π -biproduct A × H = { A × H α } α ∈ π , and prove that the automorphism has a factorization closely related to the factors A and H = { H α } α ∈ 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 ∈ π . Secondly, we consider the relationship between the automorphism group Aut π -Hopf ( A × 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 ∘ 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 ∞ then every band preserving...