J. Aust. Math. Soc.  79 (2005), 399-440
Gradings of non-graded Hamiltonian Lie algebras

A. Caranti
  Dipartimento di Matematica
  Università degli Studi di Trento
  via Sommarive 14
  I-38050 Povo (Trento)
  Italy
  caranti@science.unitn.it
and
S. Mattarei
  Dipartimento di Matematica
  Università degli Studi di Trento
  via Sommarive 14
  I-38050 Povo (Trento)
  Italy
  mattarei@science.unitn.it


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