Communications in Mathematical Physics, ISSN 0010-3616, 09/1986, Volume 105, Issue 3, pp. 375 - 384

Journal Article

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 11/2018, Volume 17, Issue 5, pp. 1065 - 1120

We study actions of Lie supergroups, in particular, the hitherto elusive notion of orbits through odd (or more general) points. Following categorical...

coadjoint action | categorical quotient | generalised point | supermanifold | Lie supergroup | Kirillov's orbit method | MATHEMATICS | UNITARY REPRESENTATIONS | SUPER | SUPERGROUPS | ORBITS | Orbital stability | Isotropy | Orbits | Representations | Existence theorems | Differential Geometry | Algebraic Geometry | Mathematics

coadjoint action | categorical quotient | generalised point | supermanifold | Lie supergroup | Kirillov's orbit method | MATHEMATICS | UNITARY REPRESENTATIONS | SUPER | SUPERGROUPS | ORBITS | Orbital stability | Isotropy | Orbits | Representations | Existence theorems | Differential Geometry | Algebraic Geometry | Mathematics

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2014, Volume 278, Issue 1, pp. 441 - 492

We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds, but enjoys much stronger permanence...

Leites’s theorem | 32C11 | Fibre product | Weil superalgebra | Mathematics, general | Weil functor | Mathematics | Superspace | Secondary 14M30 | Primary 58A50 | Inner hom | Relative supermanifold | MATHEMATICS | Leites's theorem | SUPERMANIFOLDS | Resveratrol | Differential Geometry | Algebraic Geometry

Leites’s theorem | 32C11 | Fibre product | Weil superalgebra | Mathematics, general | Weil functor | Mathematics | Superspace | Secondary 14M30 | Primary 58A50 | Inner hom | Relative supermanifold | MATHEMATICS | Leites's theorem | SUPERMANIFOLDS | Resveratrol | Differential Geometry | Algebraic Geometry

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 109, Issue 2, pp. 381 - 402

An odd deformation of a super Riemann surface $$\mathcal {S}$$ S is a deformation of $$\mathcal {S}$$ S by variables of odd parity. In this article, we study...

Geometry | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Deformation theory | Group Theory and Generalizations | Super Riemann surfaces | Complex supergeometry | 58A50 | Physics | PHYSICS, MATHEMATICAL

Geometry | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Deformation theory | Group Theory and Generalizations | Super Riemann surfaces | Complex supergeometry | 58A50 | Physics | PHYSICS, MATHEMATICAL

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2019, Volume 109, Issue 9, pp. 1939 - 1960

It is known that the supermultiplet of beta-deformations of $$\mathcal{N}=4$$ N = 4 supersymmetric Yang–Mills theory can be described in terms of the exterior...

Theoretical, Mathematical and Computational Physics | Complex Systems | Scattering amplitudes | Physics | Geometry | 81R25 | 81T13 | AdS/CFT correspondence | Representations of Lie superalgebras | Twistor theory | Supergeometry | Group Theory and Generalizations | 58A50 | 81Q60 | AdS | N=4 SYM | PHYSICS, MATHEMATICAL | MARGINAL DEFORMATIONS | OPERATORS | CFT correspondence | STRING THEORY | Algebra

Theoretical, Mathematical and Computational Physics | Complex Systems | Scattering amplitudes | Physics | Geometry | 81R25 | 81T13 | AdS/CFT correspondence | Representations of Lie superalgebras | Twistor theory | Supergeometry | Group Theory and Generalizations | 58A50 | 81Q60 | AdS | N=4 SYM | PHYSICS, MATHEMATICAL | MARGINAL DEFORMATIONS | OPERATORS | CFT correspondence | STRING THEORY | Algebra

Journal Article

6.
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Integral representations on supermanifolds: super Hodge duals, PCOs and Liouville forms

Letters in Mathematical Physics, ISSN 0377-9017, 1/2017, Volume 107, Issue 1, pp. 167 - 185

We present a few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of...

Geometry | Geometric integration theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supermanifolds and graded manifolds | 49Q15 | Group Theory and Generalizations | 58A50 | Analysis on supermanifolds or graded manifolds | Physics | 58C50 | RHAM COHOMOLOGY | PHYSICS, MATHEMATICAL | STRING THEORY

Geometry | Geometric integration theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Supermanifolds and graded manifolds | 49Q15 | Group Theory and Generalizations | 58A50 | Analysis on supermanifolds or graded manifolds | Physics | 58C50 | RHAM COHOMOLOGY | PHYSICS, MATHEMATICAL | STRING THEORY

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2017, Volume 351, Issue 3, pp. 1091 - 1126

For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason–Fourier transform. We prove an inversion formula exhibiting residue...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | SUPERMANIFOLDS | SYMMETRY CLASSES | PHYSICS, MATHEMATICAL | BEREZIN INTEGRATION | THEOREMS

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | SUPERMANIFOLDS | SYMMETRY CLASSES | PHYSICS, MATHEMATICAL | BEREZIN INTEGRATION | THEOREMS

Journal Article

Acta applicandae mathematicae, ISSN 1572-9036, 2018, Volume 160, Issue 1, pp. 129 - 167

We generalise to the Z 2 $\mathbb{Z}_{2}$ -graded set-up a practical method for inspecting the (non)removability of parameters in zero-curvature...

Supersymmetry | Computational Mathematics and Numerical Analysis | 37K25 | Removability | 58J72 | Probability Theory and Stochastic Processes | Gardner’s deformation | Mathematics | 35Q53 | Calculus of Variations and Optimal Control; Optimization | Frölicher–Nijenhuis bracket | Zero-curvature representation | Korteweg–de Vries equation | Spectral parameter | Applications of Mathematics | 58A50 | Partial Differential Equations

Supersymmetry | Computational Mathematics and Numerical Analysis | 37K25 | Removability | 58J72 | Probability Theory and Stochastic Processes | Gardner’s deformation | Mathematics | 35Q53 | Calculus of Variations and Optimal Control; Optimization | Frölicher–Nijenhuis bracket | Zero-curvature representation | Korteweg–de Vries equation | Spectral parameter | Applications of Mathematics | 58A50 | Partial Differential Equations

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 01/2012, Volume 215, Issue 1014, pp. 1 - 77

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes,...

Algebraic supergroups | MATHEMATICS

Algebraic supergroups | MATHEMATICS

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 108, Issue 9, pp. 2099 - 2137

We define the transgression functor which associates with a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle...

Geometry | Courant algebroid | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Differential graded manifold | 53D15 | Group Theory and Generalizations | 58A50 | Physics | HIGHER ANALOGS | MANIFOLDS | PHYSICS, MATHEMATICAL

Geometry | Courant algebroid | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Differential graded manifold | 53D15 | Group Theory and Generalizations | 58A50 | Physics | HIGHER ANALOGS | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 08/2016, Volume 47, pp. 212 - 245

Smooth actions of the multiplicative monoid (R,⋅) of real numbers on manifolds lead to an alternative, and for some reasons simpler, definitions of a vector...

Homogeneity structure | Graded manifold | Monoid action | Graded bundle | Holomorphic bundle | Supermanifold | MATHEMATICS | MATHEMATICS, APPLIED | Manifolds | Bundling | Maps | Mathematical analysis | Jets | Vectors (mathematics) | Manifolds (mathematics) | Monoids | Mathematics - Differential Geometry

Homogeneity structure | Graded manifold | Monoid action | Graded bundle | Holomorphic bundle | Supermanifold | MATHEMATICS | MATHEMATICS, APPLIED | Manifolds | Bundling | Maps | Mathematical analysis | Jets | Vectors (mathematics) | Manifolds (mathematics) | Monoids | Mathematics - Differential Geometry

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2013, Volume 68, pp. 27 - 58

We develop a systematic approach to contact and Jacobi structures on graded supermanifolds. In this framework, contact structures are interpreted as symplectic...

Contact structures | Lie algebroids | Symplectic manifolds | Supermanifolds | Courant algebroids | Poisson brackets | POISSON | LIE BIALGEBROIDS | JACOBI STRUCTURES | PHYSICS, MATHEMATICAL | MATHEMATICS | REDUCTION | QUANTIZATION | GEOMETRY

Contact structures | Lie algebroids | Symplectic manifolds | Supermanifolds | Courant algebroids | Poisson brackets | POISSON | LIE BIALGEBROIDS | JACOBI STRUCTURES | PHYSICS, MATHEMATICAL | MATHEMATICS | REDUCTION | QUANTIZATION | GEOMETRY

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2017, Volume 107, Issue 11, pp. 2093 - 2145

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use...

Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Index theorem | Heat kernel | 19K56 | Physics | Geometry | 35K08 | Group Theory and Generalizations | 58A50 | Supermanifold | COHOMOLOGY | POISSON MANIFOLDS | VARIABLES | SEPARATION | PHYSICS, MATHEMATICAL | STAR PRODUCTS | EQUIVALENCE | KAHLER MANIFOLD | Mathematics - Quantum Algebra

Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Index theorem | Heat kernel | 19K56 | Physics | Geometry | 35K08 | Group Theory and Generalizations | 58A50 | Supermanifold | COHOMOLOGY | POISSON MANIFOLDS | VARIABLES | SEPARATION | PHYSICS, MATHEMATICAL | STAR PRODUCTS | EQUIVALENCE | KAHLER MANIFOLD | Mathematics - Quantum Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2015, Volume 105, Issue 12, pp. 1735 - 1783

A construction of gauge-invariant observables is suggested for a class of topological field theories, the AKSZ sigma models. The observables are associated to...

Geometry | Q-manifolds | observables | Batalin–Vilkovisky formalism | 57R56 | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Topological field theory | Physics

Geometry | Q-manifolds | observables | Batalin–Vilkovisky formalism | 57R56 | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Topological field theory | Physics

Journal Article

Forum Mathematicum, ISSN 0933-7741, 11/2016, Volume 28, Issue 6, pp. 1031 - 1050

There are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops....

group functor | 18F05 | Supermanifolds | 58A50 | holonomy | 53C29 | MATHEMATICS | MATHEMATICS, APPLIED | SUPERGROUPS | Theorems | Vectors (mathematics) | Subspaces | Mathematical analysis

group functor | 18F05 | Supermanifolds | 58A50 | holonomy | 53C29 | MATHEMATICS | MATHEMATICS, APPLIED | SUPERGROUPS | Theorems | Vectors (mathematics) | Subspaces | Mathematical analysis

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 2009, Volume 59, Issue 9, pp. 1285 - 1305

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a...

Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry

Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 03/1985, Volume 100, Issue 1, pp. 141 - 160

Journal Article

Vietnam Journal of Mathematics, ISSN 2305-221X, 3/2016, Volume 44, Issue 1, pp. 215 - 229

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e., not “super-”) differential...

Supersymmetry | Clifford modules | Non-linear σ -models | 30F15 | Mathematics, general | Mathematics | Super Riemann surfaces | 32G15 | Dirac operators | 58A50 | Torsion | Non-linear σ-models | Mathematics - Differential Geometry

Supersymmetry | Clifford modules | Non-linear σ -models | 30F15 | Mathematics, general | Mathematics | Super Riemann surfaces | 32G15 | Dirac operators | 58A50 | Torsion | Non-linear σ-models | Mathematics - Differential Geometry

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2013, Volume 318, Issue 3, pp. 675 - 716

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | MANIFOLDS | PHYSICS, MATHEMATICAL | LIE ALGEBROIDS | GROUPOIDS | GEOMETRY

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | MANIFOLDS | PHYSICS, MATHEMATICAL | LIE ALGEBROIDS | GROUPOIDS | GEOMETRY

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 03/1985, Volume 102, Issue 1, pp. 123 - 137

Journal Article

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