Adjoint cohomology of graded Lie algebras of maximal class

Details Adjoint cohomology of graded Lie algebras of maximal class Adjoint cohomology of graded Lie algebras of maximal class

2007-09-16

arxiv.org/abs/0709.2468v1

Mathematics

Rings and Algebras

Scientific paper

We compute explicitly the adjoint cohomology of two N-graded Lie algebras of maximal class (infinite dimensional filiform Lie algebras) m_0 and m_2. It is known that up to an isomorphism there are only three N-graded Lie algebras of the maximal class. The third algebra from this list is the "positive" part L_1 of the Witt (or Virasoro) algebra and its adjoint cohomology was computed earlier by Feigin and Fukhs. We show that the total space H*(m_j,m_j) is "almost" isomorphic to the completed tensor product of the algebra m_j by scalar cohomology space H^*(m_j), j=0,2.

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