On two results of Singhof

Augustin-Liviu Mare

Displaying similar documents to “On two results of Singhof”

Braided tensor product and Lie algebra in a braided category. (Produit tensoriel tressé et algèbre de Lie dans une catégorie tressée.)

Haddi, A., Hadj Nassar, S. (1999)

Beiträge zur Algebra und Geometrie

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Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

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We introduce a new class of connected solvable Lie groups called $H$ -group. Namely a $H$ -group is a connected solvable Lie group with center $Z$ such that for some $ℓ$ in the Lie algebra $h$ of $H$ , the symplectic for $B_{ℓ}$ on $h / z$ given by $ℓ ([x, y])$ is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group $G$ with center $Z$ , such that the center of $G / Rad G$ is finite, has discrete series if and only if $G$ may be written as $G = H S^{'}$ , $H \cap S = Z^{0}$ , where $H$ is a $H$ -group with...

Higher-dimensional algebra. VI: Lie 2-algebras.

Baez, John C., Crans, Alissa S. (2004)

Theory and Applications of Categories [electronic only]

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Triple automorphisms of simple Lie algebras

Deng Yin Wang, Xiaoxiang Yu (2011)

Czechoslovak Mathematical Journal

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An invertible linear map $ϕ$ on a Lie algebra $L$ is called a triple automorphism of it if $ϕ ([x, [y, z]]) = [ϕ (x), [ϕ (y), ϕ (z)]]$ for $\forall x, y, z \in L$ . Let $𝔤$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $𝔭$ an arbitrary parabolic subalgebra of $𝔤$ . It is shown in this paper that an invertible linear map $ϕ$ on $𝔭$ is a triple automorphism if and only if either $ϕ$ itself is an automorphism of $𝔭$ or it is the composition of an automorphism of $𝔭$ and an extremal map of order $2$ . ...

Higher-dimensional algebra. V: 2-Groups.

Baez, John C., Lauda, Aaron D. (2004)

Theory and Applications of Categories [electronic only]

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Invariant orders in Lie groups

Neeb, Karl-Hermann

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[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group $G$ admits a continuous invariant order if and only if its Lie algebra $L (G)$ contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If $G$ is solvable and simply connected then all pointed invariant cones $W$ in $L (G)$ are global in $G$ (a Lie wedge $W \subset L (G)$ ...

Integrating central extensions of Lie algebras via Lie 2-groups

Christoph Wockel, Chenchang Zhu (2016)

Journal of the European Mathematical Society

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The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of $π_{2}$ for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated...