Gradings of non-graded Hamiltonian Lie algebras

Details Gradings of non-graded Hamiltonian Lie algebras Gradings of non-graded Hamiltonian Lie algebras

2005-10-20

arxiv.org/abs/math/0510431v1

J. Aust. Math. Soc. 79 (2005), no. 3, 399-440

Mathematics

Rings and Algebras

36 pages, to be published in J. Austral. Math. Soc. Ser. A

Scientific paper

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 $H(2\colon\n;\omega_2)$ (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 $H(2\colon\n;\omega_2)$ with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).

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