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Atiyah classes and dg-Lie algebroids for matched pairs ; Voglaire, Yannick 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 ▲] Detailed reference viewed: 135 (19 UL)Splitting theorem for Z_2^n-supermanifolds ; ; Poncin, Norbert in Journal of Geometry & Physics (2016), 110 Detailed reference viewed: 120 (20 UL)A bicategory of reduced orbifolds from the point of view of differential geometry Tommasini, Matteo in Journal of Geometry & Physics (2016), 108 Detailed reference viewed: 51 (0 UL)Commutative n-ary superalgebras with an invariant skew-symmetric form Vishnyakova, Elizaveta 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 ▲] Detailed reference viewed: 40 (0 UL)Graded geometry in gauge theories and beyond Salnikov, Vladimir 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 ▲] Detailed reference viewed: 62 (3 UL)From hypercomplex to holomorphic symplectic structures Hong, Wei in Journal of Geometry & Physics (2015), 96 Detailed reference viewed: 109 (11 UL)SUSY-structures, representations, and the Peter-Weyl theorem for S^1|1 Kwok, Stephen ; ; in Journal of Geometry & Physics (2015) Detailed reference viewed: 40 (1 UL)On the category of Lie n-algebroids Bonavolontà, Giuseppe ; Poncin, Norbert in Journal of Geometry & Physics (2013), 73 Detailed reference viewed: 167 (24 UL)Equivariant quantization of orbifolds Poncin, Norbert ; ; in Journal of Geometry & Physics (2010), 60(9), 1103--1111 Detailed reference viewed: 109 (2 UL)Superizations of Cahen-Wallach symmetric spaces and spin representations of the Heisenberg algebra Santi, Andrea in Journal of Geometry & Physics (2010), 60(2), 295--325 Detailed reference viewed: 89 (1 UL)A first approximation for quantization of singular spaces Poncin, Norbert ; ; in Journal of Geometry & Physics (2009), 59(4), 503--518 Detailed reference viewed: 97 (2 UL)Coherent state embeddings, polar divisors and Cauchy formulas ; Schlichenmaier, Martin in Journal of Geometry & Physics (2000), 34 Detailed reference viewed: 53 (0 UL) |
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