Displaying similar documents to “Bialgebra structures on a real semisimple Lie algebra.”

Poisson-Lie groupoids and the contraction procedure

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...

Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Liping Sun, Wende Liu (2017)

Open Mathematics

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According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....

Underlying Lie algebras of quadratic Novikov algebras

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 10 .

Truncated Lie groups and almost Klein models

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.