200 citations · 1.6k across the 65 of their papers we have counts for
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On the coadjoint Virasoro action
Anton Alekseev, Eckhard Meinrenken
The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of conjugacy classes in a certain open subset of th…
Linearization of Poisson Lie group structures
Anton Alekseev, Eckhard Meinrenken
We show that for any coboundary Poisson Lie group G, the Poisson structure on G^* is linearizable at the group unit. This strengthens a result of Enriquez-Etingof-Marshall, who had…
Current algebra functors and extensions
Anton Alekseev, Pavol Severa, Cornelia Vizman
We show how the fundamental cocycles on current Lie algebras and the Lie algebra of symmetries for the sigma model are obtained via the current algebra functors. We present current…
Equivariant cohomology and current algebras
Anton Alekseev, Pavol Severa
Let M be a manifold and g a Lie algebra acting on M. Differential forms Omega(M) carry a natural action of Lie derivatives L(x) and contractions I(x) of fundamental vector fields f…
The Atiyah algebroid of the path fibration over a Lie group
A. Alekseev, E. Meinrenken
Let G be a connected Lie group, LG its loop group, and PG->G the principal LG-bundle defined by quasi-periodic paths in G. This paper is devoted to differential geometry of the Ati…
Ginzburg-Weinstein via Gelfand-Zeitlin
A. Alekseev, E. Meinrenken
Let U(n) be the unitary group, and the dual of its Lie algebra, equipped with the Kirillov Poisson structure. In their 1983 paper, Guillemin-Sternberg introduced a densely…
Equivariant cohomology and the Maurer-Cartan equation
A. Alekseev, E. Meinrenken
Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isom…
Manin pairs and moment maps
Anton Alekseev, Yvette Kosmann-Schwarzbach
A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, that…
Group-valued equivariant localization
Anton Alekseev, Eckhard Meinrenken, Chris Woodward
We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of…
The non-commutative Weil algebra
Anton Alekseev, Eckhard Meinrenken
Let G be a connected Lie group with Lie algebra g. The Duflo map is a vector space isomorphism between the symmetric algebra S(g) and the universal enveloping algebra U(g) which, a…
Duistermaat-Heckman distributions for group valued moment maps
Anton Alekseev, Eckhard Meinrenken, Chris Woodward
We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by application…