Filtering bases and cohomology of nilpotent subalgebras of Witt and sl2 Lie algebras
F. V. Weinstein
Abstract
We study the cohomology with trivial coefficients of Lie algebras Lk of the polynomial vector fields on the line with zero k-jet, (k>=1), and the cohomology of the similar subalgebras Lk of the polynomial loops algebra sl2. In both cases we construct the special bases (filtering bases) in the external complexes of these algebras. A spectral sequence based on this construction allows to completely find the cohomology of Lk and Lk. We also apply the filtering bases to find the spectral resolution of the Laplace operators for algebras L1 and L0, and obtain explicit formulas for the representing cycles of homologies for algebras Lk and Lk by means of the Schur polynomials.
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