A note on central extensions of Lie groups.
Neeb, Karl-Hermann (1996)
Journal of Lie Theory
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Neeb, Karl-Hermann (1996)
Journal of Lie Theory
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Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
Benayed, Miloud, Souidi, El Mamoun (1998)
The New York Journal of Mathematics [electronic only]
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Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Pestov, Vladimir (1995)
Journal of Lie Theory
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Miloud Benayed (1998)
Extracta Mathematicae
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Zhiqi Chen (2011)
Czechoslovak Mathematical Journal
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Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension .
Vaisman, Izu (2000)
Journal of Lie Theory
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Hernández, I., Peniche, R. (2008)
International Journal of Mathematics and Mathematical Sciences
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Abdoreza R. Armakan, Mohammed Reza Farhangdoost (2017)
Czechoslovak Mathematical Journal
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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 by another hom-Lie algebra and discuss the case where 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...
Baguis, P., Stavracou, T. (2002)
International Journal of Mathematics and Mathematical Sciences
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Jan Kubarski (1991)
Revista Matemática de la Universidad Complutense de Madrid
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Georges Giraud, Michel Boyom (2004)
Open Mathematics
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We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.