# Λ-modules and holomorphic Lie algebroid connections

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1422-1441
- ISSN: 2391-5455

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topPietro Tortella. "Λ-modules and holomorphic Lie algebroid connections." Open Mathematics 10.4 (2012): 1422-1441. <http://eudml.org/doc/269694>.

@article{PietroTortella2012,

abstract = {Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and $ \equiv :Gr\Lambda \rightarrow Sym \bullet _\{\mathcal \{O\}_X \} \mathcal \{G\}$ is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on $\mathcal \{G\}$ and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.},

author = {Pietro Tortella},

journal = {Open Mathematics},

keywords = {Holomorphic Lie algebroids; Filtered algebras; Universal enveloping algebra; Lie algebroid connections; Moduli spaces of flat connections; Generalized holomorphic bundles; holomorphic Lie algebroids; filtered algebras; flat connections; generalized holomorphic bundles; Hodge filtration; characteristic ring; characteristic classes; anchor; matched pairs of Lie algebroids; twilled pairs; twilled sum; sheaves of filtered algebras; holomorphic Poisson structures},

language = {eng},

number = {4},

pages = {1422-1441},

title = {Λ-modules and holomorphic Lie algebroid connections},

url = {http://eudml.org/doc/269694},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Pietro Tortella

TI - Λ-modules and holomorphic Lie algebroid connections

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1422

EP - 1441

AB - Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and $ \equiv :Gr\Lambda \rightarrow Sym \bullet _{\mathcal {O}_X } \mathcal {G}$ is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on $\mathcal {G}$ and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.

LA - eng

KW - Holomorphic Lie algebroids; Filtered algebras; Universal enveloping algebra; Lie algebroid connections; Moduli spaces of flat connections; Generalized holomorphic bundles; holomorphic Lie algebroids; filtered algebras; flat connections; generalized holomorphic bundles; Hodge filtration; characteristic ring; characteristic classes; anchor; matched pairs of Lie algebroids; twilled pairs; twilled sum; sheaves of filtered algebras; holomorphic Poisson structures

UR - http://eudml.org/doc/269694

ER -

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