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Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Johannes Huebschmann — 2000

Banach Center Publications

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 algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...

Poisson structures on certain moduli spaces for bundles on a surface

Johannes Huebschmann — 1995

Annales de l'institut Fourier

Let Σ be a closed surface, G a compact Lie group, with Lie algebra g , and ξ : P Σ a principal G -bundle. In earlier work we have shown that the moduli space N ( ξ ) of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from N ( ξ ) onto a certain representation space Rep ξ ( Γ , G ) , in fact a diffeomorphism, with reference to suitable smooth structures C ( N ( ξ ) ) and C Rep ξ ( Γ , G ) , where Γ denotes the universal central extension of...

Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras

Johannes Huebschmann — 1998

Annales de l'institut Fourier

For any Lie-Rinehart algebra ( A , L ) , B(atalin)-V(ilkovisky) algebra structures on the exterior A -algebra Λ A L correspond bijectively to right ( A , L ) -module structures on A ; likewise, generators for the Gerstenhaber algebra Λ A L correspond bijectively to right ( A , L ) -connections on A . When L is projective as an A -module, given a B-V algebra structure on Λ A L , the homology of the B-V algebra ( Λ A L , ) coincides with the homology of L with coefficients in A with reference to the right ( A , L ) -module structure determined by . When...

Singular Poisson-Kähler geometry of certain adjoint quotients

Johannes Huebschmann — 2007

Banach Center Publications

The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.

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