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See detailAtiyah classes and dg-Lie algebroids for matched pairs
Batakidis, Panagiotis; Voglaire, Yannick UL

in Journal of Geometry & Physics (2017)

For every Lie pair $(L,A)$ of algebroids we construct a dg-manifold structure on the $\ZZ$-graded manifold $\M=L[1]\oplus L/A$ such that the inclusion $\iota: A[1] \to \M$ and the projection $p:\M\to L[1 ... [more ▼]

For every Lie pair $(L,A)$ of algebroids we construct a dg-manifold structure on the $\ZZ$-graded manifold $\M=L[1]\oplus L/A$ such that the inclusion $\iota: A[1] \to \M$ and the projection $p:\M\to L[1]$ are morphisms of dg-manifolds. The vertical tangent bundle $T^p\M$ then inherits a structure of dg-Lie algebroid over $\M$. When the Lie pair comes from a matched pair of Lie algebroids, we show that the inclusion $\iota$ induces a quasi-isomorphism that sends the Atiyah class of this dg-Lie algebroid to the Atiyah class of the Lie pair. We also show how (Atiyah classes of) Lie pairs and dg-Lie algebroids give rise to (Atiyah classes of) dDG-algebras. [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 detailA bicategory of reduced orbifolds from the point of view of differential geometry
Tommasini, Matteo UL

in Journal of Geometry & Physics (2016), 108

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See detailCommutative n-ary superalgebras with an invariant skew-symmetric form
Vishnyakova, Elizaveta UL

in Journal of Geometry & Physics (2015), 98

We study nn-ary commutative superalgebras and L∞L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie ... [more ▼]

We study nn-ary commutative superalgebras and L∞L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their nn-ary generalizations, commutative associative and Jordan algebras with an invariant form. We give a classification of anti-commutative mm-dimensional (m−3)(m−3)-ary algebras with an invariant form, and a classification of real simple mm-dimensional Lie (m−3)(m−3)-algebras with a positive definite invariant form up to isometry. Furthermore, we develop the Hodge Theory for L∞L∞-algebras with a symmetric invariant form, and we describe quasi-Frobenius structures on skew-symmetric nn-ary algebras. [less ▲]

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See detailFrom hypercomplex to holomorphic symplectic structures
Hong, Wei UL

in Journal of Geometry & Physics (2015), 96

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See detailSUSY-structures, representations, and the Peter-Weyl theorem for S^1|1
Kwok, Stephen UL; Carmeli, C.; Fioresi, R.

in Journal of Geometry & Physics (2015)

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See detailGraded geometry in gauge theories and beyond
Salnikov, Vladimir UL

in Journal of Geometry & Physics (2015)

We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to ... [more ▼]

We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q -manifolds introducing thus the concept of equivariant Q -cohomology. Using this concept we describe a procedure for analysis of gauge symmetries of given functionals as well as for constructing functionals (sigma models) invariant under an action of some gauge group. As the main example of application of these constructions we consider the twisted Poisson sigma model. We obtain it by a gauging-type procedure of the action of an essentially infinite dimensional group and describe its symmetries in terms of classical differential geometry. We comment on other possible applications of the described concept including the analysis of supersymmetric gauge theories and higher structures. [less ▲]

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See detailOn the category of Lie n-algebroids
Bonavolontà, Giuseppe UL; Poncin, Norbert UL

in Journal of Geometry & Physics (2013), 73

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See detailSuperizations of Cahen-Wallach symmetric spaces and spin representations of the Heisenberg algebra
Santi, Andrea UL

in Journal of Geometry & Physics (2010), 60(2), 295--325

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See detailEquivariant quantization of orbifolds
Poncin, Norbert UL; Radoux, Fabian; Wolak, Robert

in Journal of Geometry & Physics (2010), 60(9), 1103--1111

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See detailA first approximation for quantization of singular spaces
Poncin, Norbert UL; Radoux, Fabian; Wolak, Robert

in Journal of Geometry & Physics (2009), 59(4), 503--518

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See detailCoherent state embeddings, polar divisors and Cauchy formulas
Berceanu, Stefan; Schlichenmaier, Martin UL

in Journal of Geometry & Physics (2000), 34

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