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Gradings of non-graded Hamiltonian Lie algebras

Andrea Caranti·Sandro Mattarei
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Abstract

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras $H(2\colon\n;ω_2)$ (of dimension one less than a power of $p$) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of $H(2\colon\n;ω_2)$ with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).

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Andrea Caranti, Sandro Mattarei. 2005-10-20. Gradings of non-graded Hamiltonian Lie algebras. https://arxiv.org/abs/math/0510431

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