Reviews in Mathematical Physics, ISSN 0129-055X, 10/2016, Volume 28, Issue 9, p. 1650021

We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in...

supersymmetry | matrix models | N Q-manifolds | multisymplectic geometry | higher gauge theory | Analysis | Algebra

supersymmetry | matrix models | N Q-manifolds | multisymplectic geometry | higher gauge theory | Analysis | Algebra

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2014, Volume 412, Issue 2, pp. 613 - 619

A compact convex subset K of a topological linear space is called a Keller compactum if it is affinely homeomorphic to an infinite-dimensional compact convex...

Hyperspace | Q-manifold | Orbit space | Keller compactum | Infinite-dimensional convex set | Affine group | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISM GROUP

Hyperspace | Q-manifold | Orbit space | Keller compactum | Infinite-dimensional convex set | Affine group | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISM GROUP

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 08/2019, Volume 142, pp. 254 - 273

Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold...

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 03/2016, Volume 101, pp. 71 - 99

Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as...

Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL

Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2014, Volume 86, pp. 497 - 533

We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space–time...

Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra

Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra

Journal Article

Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 8/2018, Volume 302, Issue 1, pp. 88 - 129

We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical...

Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Q-MANIFOLDS | MORPHISMS

Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Q-MANIFOLDS | MORPHISMS

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 10/2014, Volume 25, Issue 5, pp. 1122 - 1134

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid...

Representation up to homotopy | Q-manifold | Graded manifold | Graded vector bundle | Lie algebroid | MATHEMATICS | BRACKETS | COHOMOLOGY | DEFORMATIONS | Mathematics - Differential Geometry

Representation up to homotopy | Q-manifold | Graded manifold | Graded vector bundle | Lie algebroid | MATHEMATICS | BRACKETS | COHOMOLOGY | DEFORMATIONS | Mathematics - Differential Geometry

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12

We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle....

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of...

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

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

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 01/2015, Volume 12, Issue 1, pp. 1550006 - 1-1550006-26

A Q-manifold is a graded manifold endowed with a vector field of degree 1 squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in...

Q-manifolds | gauge theories | characteristic classes | PHYSICS, MATHEMATICAL | Manifolds | Bundling | Construction | Categories | Lie groups | Fields (mathematics) | Topology | Gages | Fibers

Q-manifolds | gauge theories | characteristic classes | PHYSICS, MATHEMATICAL | Manifolds | Bundling | Construction | Categories | Lie groups | Fields (mathematics) | Topology | Gages | Fibers

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2010, Volume 94, Issue 3, pp. 243 - 261

An odd vector field Q on a supermanifold M is called homological, if Q 2 = 0. The operator of Lie derivative L Q makes the algebra of smooth tensor fields on M...

Geometry | Q -manifolds | gauge theories | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | 57R32 | characteristic classes | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Physics | Q-manifolds | LIE | PHYSICS, MATHEMATICAL | ALGEBRA

Geometry | Q -manifolds | gauge theories | Theoretical, Mathematical and Computational Physics | 81T70 | Group Theory and Generalizations | 57R32 | characteristic classes | Statistical Physics, Dynamical Systems and Complexity | 58A50 | Physics | Q-manifolds | LIE | PHYSICS, MATHEMATICAL | ALGEBRA

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2015, Volume 11

We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as...

Homogeneity structures | Lie algebroids | Lie groupoids | Graded manifolds | homogeneity structures | BRACKETS | ALGEBROIDS | INTEGRABILITY | graded manifolds | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | JACOBI | INTEGRATION | Q-MANIFOLDS | FORMALISM | CONTACT GROUPOIDS

Homogeneity structures | Lie algebroids | Lie groupoids | Graded manifolds | homogeneity structures | BRACKETS | ALGEBROIDS | INTEGRABILITY | graded manifolds | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | JACOBI | INTEGRATION | Q-MANIFOLDS | FORMALISM | CONTACT GROUPOIDS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 01/2015, Volume 87, pp. 422 - 431

We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant...

[formula omitted]-manifolds | Twisted Poisson sigma model | Courant algebroids | Equivariant cohomology | Gauging | Q-manifolds | MATHEMATICS | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics

[formula omitted]-manifolds | Twisted Poisson sigma model | Courant algebroids | Equivariant cohomology | Gauging | Q-manifolds | MATHEMATICS | PHYSICS, MATHEMATICAL | Mathematical Physics | Mathematics

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/2012, Volume 140, Issue 8, pp. 2855 - 2872

We show that a well-known result on solutions of the Maurer— Cartan equation extends to arbitrary (inhomogeneous) odd forms: any such form with values in a Lie...

Geologic supergroups | Algebra | Mathematical theorems | Vector fields | Abstract algebra | Coordinate systems | Mathematical constants | Mathematics | Curvature | Mathematical transitivity | Q-manifolds | Lie algebroids | Multiplicative integral | Homological vector fields | Lie superalgebras | Differential forms | Maurer-Cartan equation | Supermanifolds | Quillen's superconnection | MATHEMATICS | multiplicative integral | MATHEMATICS, APPLIED | supermanifolds | homological vector fields | differential forms

Geologic supergroups | Algebra | Mathematical theorems | Vector fields | Abstract algebra | Coordinate systems | Mathematical constants | Mathematics | Curvature | Mathematical transitivity | Q-manifolds | Lie algebroids | Multiplicative integral | Homological vector fields | Lie superalgebras | Differential forms | Maurer-Cartan equation | Supermanifolds | Quillen's superconnection | MATHEMATICS | multiplicative integral | MATHEMATICS, APPLIED | supermanifolds | homological vector fields | differential forms

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 5, pp. 729 - 759

A Q -manifold M is a supermanifold endowed with an odd vector field Q squaring to zero. The Lie derivative L Q along Q makes the algebra of smooth tensor...

[formula omitted]-manifolds | Gauge theories | Characteristic classes | Q-manifolds | MATHEMATICS, APPLIED | COHOMOLOGY | MASTER EQUATION | LIE ALGEBROIDS | POISSON MANIFOLD | MODULAR CLASS | QUANTIZATION | PHYSICS, MATHEMATICAL | GEOMETRY

[formula omitted]-manifolds | Gauge theories | Characteristic classes | Q-manifolds | MATHEMATICS, APPLIED | COHOMOLOGY | MASTER EQUATION | LIE ALGEBROIDS | POISSON MANIFOLD | MODULAR CLASS | QUANTIZATION | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 10/2009, Volume 242, Issue 2, pp. 311 - 332

We approach Mackenzie's LA-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds....

Q-manifolds | Lie algebroids | Lie groupoids | Simplicial manifolds | Equivariant cohomology | MATHEMATICS | simplicial manifolds | DOUBLE LIE ALGEBROIDS | SPACES | 2ND-ORDER GEOMETRY | MAP | equivariant cohomology

Q-manifolds | Lie algebroids | Lie groupoids | Simplicial manifolds | Equivariant cohomology | MATHEMATICS | simplicial manifolds | DOUBLE LIE ALGEBROIDS | SPACES | 2ND-ORDER GEOMETRY | MAP | equivariant cohomology

Journal Article

Topology and its Applications, ISSN 0166-8641, 2006, Volume 153, Issue 11, pp. 1699 - 1704

We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube...

Soft map | Q-manifold | Convex body | Constant width | MATHEMATICS | MATHEMATICS, APPLIED | constant width | soft map | convex body

Soft map | Q-manifold | Convex body | Constant width | MATHEMATICS | MATHEMATICS, APPLIED | constant width | soft map | convex body

Journal Article

Archivum Mathematicum, ISSN 0044-8753, 2017, Volume 53, Issue 4, pp. 203 - 219

Archivum Mathematicum, vol. 53 (2017), issue 4, pp. 203-219 A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion...

Modular classes | Higher Poisson manifolds | Q-manifolds | Characteristic classes | algebroids

Modular classes | Higher Poisson manifolds | Q-manifolds | Characteristic classes | algebroids

Journal Article

Fundamenta Mathematicae, ISSN 0016-2736, 2001, Volume 166, Issue 3, pp. 209 - 232

Journal Article

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