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Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere

Joël Merker, Masoud Sabzevari (2012)

Open Mathematics

We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.

Explicit representations of classical Lie superalgebras in a Gelfand-Zetlin basis

N. I. Stoilova, J. Van der Jeugt (2011)

Banach Center Publications

An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for 𝔰𝔬(n) and 𝔰𝔭(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly only for 𝔤𝔩(1|n), 𝔤𝔩(2|2), 𝔬𝔰𝔭(3|2) and for the so called essentially typical representations of 𝔤𝔩(m|n)....

Exponentiations over the quantum algebra U q ( s l 2 ( ℂ ) )

Sonia L’Innocente, Françoise Point, Carlo Toffalori (2013)

Confluentes Mathematici

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra U q ( s l 2 ( ℂ ) ) . We discuss two cases, according to whether the parameter q is a root of unity. We show that the universal enveloping algebra of s l 2 ( ℂ ) embeds in a non-principal ultraproduct of U q ( s l 2 ( ℂ ) ) , where q varies over the primitive roots of unity.

Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai, Xuping Xu, Hai Lin, Derong Liu (2007)

International Journal of Applied Mathematics and Computer Science

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show...

Extensions centrales d'algèbres de Lie

Christian Kassel, Jean-Louis Loday (1982)

Annales de l'institut Fourier

Soient k un anneau commutatif et A une k -algèbre associative quelconque. Nous calculons le groupe d’homologie H 2 ( 𝔰 l n ( A ) , k ) de la k -algèbre de Lie 𝔰 l n ( A ) des matrices de “trace nulle” sur A . Le groupe ainsi déterminé est un groupe d’homologie d’un complexe inspiré d’A. Connes; il est isomorphe à Ω A / k 1 / d A lorsque A est commutative. Nous obtenons également des résultats pour un groupe d’homologie relative associé à une surjection de k -algèbres. Les démonstrations utilisent la classification des extensions centrales et des...

Extensions of hom-Lie algebras in terms of cohomology

Abdoreza R. Armakan, Mohammed Reza Farhangdoost (2017)

Czechoslovak Mathematical Journal

We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra 𝔤 by another hom-Lie algebra 𝔥 and discuss the case where 𝔥 has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction...

Extremal projectors in the semi-classical case

Sophie Chemla (1997)

Annales de l'institut Fourier

Using extremal projectors, Zhelobenko solved extremal equations in a generic Verma module of a complex semi-simple Lie algebra. We will solve similar equations in the semi-classical case. Our proof will be geometric. In the appendix, we give a factorization for the extremal projector of the Virasoro algebra in the semi-classical case.

Currently displaying 441 – 460 of 1861