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The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups in the sense of [Get09, Hen08]. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of $π_{2}$ for each finite-dimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated to each finite-dimensional...

Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity

Magdalena Zielenkiewicz (2014)

Open Mathematics

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of...

Internal categories in a left exact cosimplicial category.

Pataraia, D. (1997)

Georgian Mathematical Journal

Internal functionals and bundle duals.

Kitchen, Joseph W., Robbins, David A. (1984)

International Journal of Mathematics and Mathematical Sciences

Intersection cohomology of cs-spaces and Zeeman's filtration.

Nathan Habegger, Leslie Saper (1991)

Inventiones mathematicae

Intersection cohomology of reductive varieties

Roy Joshua, Michel Brion (2004)

Journal of the European Mathematical Society

We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.