References of "Grabowski, Janusz"
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See detailPre-Courant algebroids
Bruce, Andrew UL; Grabowski, Janusz

in Journal of Geometry and Physics (2019), 142

Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold description of pre-Courant algebroids and some ... [more ▼]

Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold description of pre-Courant algebroids and some direct consequences thereof. In particular, we define symplectic almost Lie 2-algebroids and show how they correspond to pre-Courant algebroids. We give the definition of (sub-)Dirac structures and study the naïve quasi-cochain complex within the setting of supergeometry. Moreover, the framework of supermanifolds allows us to economically define and work with pre-Courant algebroids equipped with a compatible non-negative grading. VB-Courant algebroids are natural examples of what we call weighted pre-Courant algebroids and our approach drastically simplifies working with them. [less ▲]

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See detailRepresentations up to Homotopy from Weighted Lie Algebroids
Bruce, Andrew UL; Grabowski, Janusz; Vitagliano, Luca

in Journal of Lie Theory (2018), 28(3), 715-737

Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB-algebroid. There ... [more ▼]

Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB-algebroid. There is a close relation between two term representations up to homotopy of Lie algebroids and VB-algebroids. In this paper we show how this relation generalises to weighted Lie algebroids and in doing so we uncover new and natural examples of higher term representations up to homotopy of Lie algebroids. Moreover, we show how the van Est theorem generalises to weighted objects. [less ▲]

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See detailOn the Concept of a Filtered Bundle
Bruce, Andrew UL; Grabowska, Katarzyna; Grabowski, Janusz

in International Journal of Geometric Methods in Modern Physics (2018), 15

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of ... [more ▼]

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include affine bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and classical field theory. We also present the notion of double filtered bundles which provide natural generalizations of double vector bundles and double affine bundles. Furthermore, we show that the linearization of a filtered bundle — which can be seen as a partial polarization of the admissible changes of local coordinates — is well defined. [less ▲]

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See detailRemarks on Contact and Jacobi Geometry
Bruce, Andrew UL; Grabowska, Katarzyna; Grabowski, Janusz

in Symmetry, Integrability and Geometry: Methods and Applications [=SIGMA] (2017), 13(059), 22

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and ... [more ▼]

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,ℝ)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory. [less ▲]

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See detailSplitting theorem for Z_2^n-supermanifolds
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert UL

in Journal of Geometry & Physics (2016), 110

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See detailThe category of Z_2^n-supermanifolds
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert UL

in Journal of Mathematical Physics (2016), 57(7), 16

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See detailRemarks on contact and Jacobi geometry
Bruce, Andrew UL; Grabowska, Katarzyna; Grabowski, Janusz

E-print/Working paper (2016)

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and ... [more ▼]

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and Kirillov algebroids, i.e. homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1, R)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. In this sense, the properly understood concept of a Jacobi structure is a specialisation rather than a generalisation of a Poission structure. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, as well as give new insight in the theory. For instance, we describe the structure of Lie groupoids with a compatible principal G-bundle structure and the ‘integrating objects’ for Kirillov algebroids, define canonical contact groupoids, and show that any contact groupoid has a canonical realisation as a contact subgroupoid of the latter. [less ▲]

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See detailIntegration on colored supermanifolds
Grabowski, Janusz; Kwok, Stephen UL; Poncin, Norbert UL

E-print/Working paper (2016)

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See detailZ_2^n-Supergeometry II: Batchelor-Gawedzki Theorem
Covolo, Tiffany UL; Grabowski, Janusz; Poncin, Norbert UL

E-print/Working paper (2014)

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See detailZ_2^n-Supergeometry I: Manifolds and Morphisms
Covolo, Tiffany UL; Grabowski, Janusz; Poncin, Norbert UL

E-print/Working paper (2014)

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See detailThe supergeometry of Loday algebroids
Grabowski, Janusz; Khudaverdyan, David UL; Poncin, Norbert UL

in Journal of Geometric Mechanics (2013), 5(2), 185--213

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See detailLie superalgebras of differential operators
Grabowski, Janusz; Kotov, Alexei; Poncin, Norbert UL

in Journal of Lie Theory (2013), 23(1), 35--54

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See detailGeometric structures encoded in the Lie structure of an Atiyah algebroid
Grabowski, Janusz; Kotov, Alexei; Poncin, Norbert UL

in Transformation Groups (2011), 16(1), 137--160

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See detailThe Lie superalgebra of a supermanifold
Grabowski, Janusz; Kotov, Alexei; Poncin, Norbert UL

in Journal of Lie Theory (2010), 20(4), 739--749

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See detailOn quantum and classical Poisson algebras
Grabowski, Janusz; Poncin, Norbert UL

in Banach Center Publications (2007), 76

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See detailDerivations of the Lie algebras of differential operators
Grabowski, Janusz; Poncin, Norbert UL

in Indagationes Mathematicae (2005), 16(2), 181--200

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See detailLie algebraic characterization of manifolds
Grabowski, Janusz; Poncin, Norbert UL

in Central European Journal of Mathematics (2004), 2(5), 811--825

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See detailAutomorphisms of quantum and classical Poisson algebras
Grabowski, Janusz; Poncin, Norbert UL

in Compositio Mathematica (2004), 140(2), 511-527

Detailed reference viewed: 65 (8 UL)