Displaying similar documents to “Poisson-Lie groupoids and the contraction procedure”

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 .

Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras

Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar (2024)

Czechoslovak Mathematical Journal

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This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras....

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

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We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.