53 citations · 287 across the 51 of their papers we have counts for
17 papers · 1 filter
Quasi Poisson structures, weakly quasi Hamiltonian structures, and Poisson geometry of various moduli spaces
Johannes Huebschmann
Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tens…
Finite-dimensional construction of self-duality and related moduli spaces over a closed Riemann surface as stratified holomorphic symplectic spaces
Johannes Huebschmann
In terms of appropriate extended moduli spaces, we develop a finite-dimensional construction of the self-duality and related moduli spaces over a closed Riemann surface as stratifi…
Yang-Mills moduli spaces over an orientable closed surface via Fréchet reduction
Tobias Diez, Johannes Huebschmann
Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relativ…
Kaehler structures on T*G having as underlying symplectic form the standard one
Johannes Huebschmann, Karl Leicht
For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translatio…
Multi derivation Maurer-Cartan algebras and sh-Lie-Rinehart algebras
Johannes Huebschmann
We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer-Cartan algebra-the familiar differential graded algebra of alternating forms o…
Poisson cohomology and quantization
Johannes Huebschmann
Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of Kähler differentials o…
Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras
Johannes Huebschmann
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR a…
Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras
Johannes Huebschmann
Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra…
Kirillov's character formula, the holomorphic Peter-Weyl theorem, and the Blattner-Kostant-Sternberg pairing
Johannes Huebschmann
Let K be a compact Lie group, endowed with a bi-invariant Riemannian metric. The complexification G of K inherits a Kaehler structure having twice the kinetic energy of the metric…
Stratified Kaehler structures on adjoint quotients
Johannes Huebschmann
Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its pot…
Relative homological algebra, equivariant de Rham theory, and Koszul duality
Johannes Huebschmann
Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, an…
Higher homotopies and Maurer-Cartan algebras: Quasi-Lie-Rinehart, Gerstenhaber, and Batalin-Vilkovisky algebras
Johannes Huebschmann
Higher homotopy generalizations of Lie-Rinehart algebras, Gerstenhaber-, and Batalin-Vilkovisky algebras are explored. These are defined in terms of various antisymmetric bilinear…
Severi varieties and holomorphic nilpotent orbits
Johannes Huebschmann
Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular…
Kaehler spaces, nilpotent orbits, and singular reduction
Johannes Huebschmann
For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarization…
Singularities and Poisson geometry of certain representation spaces
Johannes Huebschmann
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases…
Rinehart complexes and Batalin-Vilkovisky algebras
Johannes Huebschmann
For a Lie-Rinehart algebra (A,L) such that, as an A-module, L is finitely generated and projective of finite constant rank, the relationship between generators of the Gerstenhaber…
Twilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebras
Johannes Huebschmann
Twilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR alg…