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Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras

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arxiv 2003.12608 v1 pith:I4Y57AXD submitted 2020-03-27 math.RA

Helena Albuquerque , Elisabete Barreiro , Saïd Benayadi , Mohamed Boucetta , José M. Sánchez This is my paper · ORCID
classification math.RA
keywords oscillatoralgebraalgebrasbialgebrastructuresleibnizsymmetricpoisson
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Oscillator Lie algebras are the only non commutative solvable Lie algebras which carry a bi-invariant Lorentzian metric. In this paper, we determine all the Poisson structures, and in particular, all symmetric Leibniz algebra structures whose underlying Lie algebra is an oscillator Lie algebra. We give also all the symmetric Leibniz bialgebra structures whose underlying Lie bialgebra structure is a Lie bialgebra structure on an oscillator Lie algebra. We derive some geometric consequences on oscillator Lie groups.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  3. Optimization Strategies for Parallel Computation of Skylines

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    Parallel skyline computation can be sped up by sharing strong tuples across partitions and replacing the final sequential cleanup with a parallel pass.

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