Cohomology Of Infinite-dimensional Lie Algebras Research Articles

Associative algebra twisted bundles over compact topological spaces

For the associative algebra A(g) of an infinite-dimensional Lie algebra g, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic completion of the space of formal series in complex parameters, sections are provided by rational functions with prescribed analytic properties. Homotopical invariance as well as covariance in terms of trivial bundles of twisted A(g)-bundles is proven. Further applications of the paper's results useful for studies of the cohomology of infinite-dimensional Lie algebras on smooth manifolds, K-theory, as well as for purposes of conformal field theory, deformation theory [10,14,15], and the theory of foliations are mentioned.

The homology of graded infinite-dimensional Lie algebras in connection with Macdonald identities

D. Fucks' monograph devoted to the cohomology of infinite-dimensional Lie algebras contains an error in calculating the homology of a graded affine Kac-Moody algebra of type A n (1) , so that the proof of the corresponding Macdonald identity, which is based on that calculation, is incorrect. In the present paper, a revised proof is suggested.

Filtering bases, cohomology of infinite-dimensional Lie algebras, and Laplace operators

Filtering bases, cohomology of infinite-dimensional Lie algebras, and Laplace operators

Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations

A theory of characteristic classes of foliations is discussed which is based on the cohomology of infinite-dimensional Lie algebras. One of the original results of the article is a theorem stating that the characteristic classes are nontrivial.

Cohomology of infinite-dimensional Lie algebras and Laplace operators

Cohomology of infinite-dimensional Lie algebras and Laplace operators

Upper bounds for cohomology of infinite-dimensional Lie algebras

Upper bounds for cohomology of infinite-dimensional Lie algebras