Rendiconti del Circolo Matematico di Palermo, ISSN 0009-725X, 12/2018, Volume 67, Issue 3, pp. 409 - 419

...Rend. Circ. Mat. Palermo, II. Ser (2018) 67:409–419 https://doi.org/10.1007/s12215-017-0322-x On equivariant formal deformation theory Stefan Schröer 1...

Formal deformation theory | Fibered categories | Group actions

Formal deformation theory | Fibered categories | Group actions

Journal Article

2017, Mathematical surveys and monographs, ISBN 1470435691, Volume 221, 2 volumes

Book

Georgian mathematical journal, ISSN 1572-9176, 2018, Volume 25, Issue 4, pp. 529 - 544

Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero...

Kuranishi method | Deformation theory | 58K60 | formal deformation | 32S60 | 16S80 | 13D10 | 14B12 | 32G05 | 14B07 | 14D15 | deformation controlled by a differential graded Lie algebra | miniversal deformation | 32G08 | COMPLEX | YANG-MILLS CONNECTIONS | BUNDLES | SINGULARITIES | COALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | SURFACE | GEOMETRY

Kuranishi method | Deformation theory | 58K60 | formal deformation | 32S60 | 16S80 | 13D10 | 14B12 | 32G05 | 14B07 | 14D15 | deformation controlled by a differential graded Lie algebra | miniversal deformation | 32G08 | COMPLEX | YANG-MILLS CONNECTIONS | BUNDLES | SINGULARITIES | COALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | SURFACE | GEOMETRY

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 2984 - 3047

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold...

Deformations | Secondary 13D10 | Deformations of complex structures | 53C55 | Primary 32G05 | Mathematics | 14D15 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hermitian and Kählerian manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Deformations and infinitesimal methods | Formal methods | NUMBERS | Hermitian and Kahlerian manifolds | METRICS | EXTENSION | FORMULA | MATHEMATICS | COMPACT KAHLER MANIFOLD | CONE | GEOMETRY

Deformations | Secondary 13D10 | Deformations of complex structures | 53C55 | Primary 32G05 | Mathematics | 14D15 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hermitian and Kählerian manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Deformations and infinitesimal methods | Formal methods | NUMBERS | Hermitian and Kahlerian manifolds | METRICS | EXTENSION | FORMULA | MATHEMATICS | COMPACT KAHLER MANIFOLD | CONE | GEOMETRY

Journal Article

2014, Mathematical surveys and monographs, ISBN 9781470410148, Volume no. 195., ix, 387

Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties...

Abelian varieties | Multiplication, Complex | Lifting theory

Abelian varieties | Multiplication, Complex | Lifting theory

Book

Reviews in Mathematical Physics, ISSN 0129-055X, 02/2005, Volume 17, Issue 1, pp. 15 - 75

In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction...

States | Morita equivalence | Representation theory | Deformation quantization | COTANGENT BUNDLES | RINGS | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | morita equivalence | ANALYTIC-FUNCTIONS | states | FORMAL MORITA EQUIVALENCE | NONCOMMUTATIVE GAUGE-THEORY | deformation quantization | GNS REPRESENTATIONS | CONSTRUCTION | representation theory | FEDOSOV STAR PRODUCTS | HILBERT-SPACE

States | Morita equivalence | Representation theory | Deformation quantization | COTANGENT BUNDLES | RINGS | QUANTUM-FIELD THEORY | PHYSICS, MATHEMATICAL | morita equivalence | ANALYTIC-FUNCTIONS | states | FORMAL MORITA EQUIVALENCE | NONCOMMUTATIVE GAUGE-THEORY | deformation quantization | GNS REPRESENTATIONS | CONSTRUCTION | representation theory | FEDOSOV STAR PRODUCTS | HILBERT-SPACE

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2007, Volume 82, Issue 2, pp. 153 - 175

We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras...

Geometry | 53D55 | Mathematical and Computational Physics | 53D10 | Group Theory and Generalizations | symbol calculus | non-formal deformation quantization | star exponential functions | Physics | Statistical Physics | 46L65 | independence of ordering principle | Non-formal deformation quantization | Symbol calculus | Independence of ordering principle | Star exponential functions | ELEMENTS | FRECHET-POISSON ALGEBRAS | LIE-ALGEBRA | EXPONENTIALS | STAR-PRODUCTS | PHYSICS, MATHEMATICAL

Geometry | 53D55 | Mathematical and Computational Physics | 53D10 | Group Theory and Generalizations | symbol calculus | non-formal deformation quantization | star exponential functions | Physics | Statistical Physics | 46L65 | independence of ordering principle | Non-formal deformation quantization | Symbol calculus | Independence of ordering principle | Star exponential functions | ELEMENTS | FRECHET-POISSON ALGEBRAS | LIE-ALGEBRA | EXPONENTIALS | STAR-PRODUCTS | PHYSICS, MATHEMATICAL

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2004, Volume 182, Issue 2, pp. 204 - 277

In this paper we define a cohomology theory for an arbitrary K-linear semistrict semigroupal 2-category ( C...

Pseudofunctors | Formal deformation | Monoidal 2-categories | 4-MANIFOLD INVARIANTS | MATHEMATICS | monoidal 2-categories | pseudofunctors | BICATEGORIES | formal deformation | 3-MANIFOLDS | STATE-SUM INVARIANTS | SPHERICAL 2-CATEGORIES | HOPF | CATEGORIES

Pseudofunctors | Formal deformation | Monoidal 2-categories | 4-MANIFOLD INVARIANTS | MATHEMATICS | monoidal 2-categories | pseudofunctors | BICATEGORIES | formal deformation | 3-MANIFOLDS | STATE-SUM INVARIANTS | SPHERICAL 2-CATEGORIES | HOPF | CATEGORIES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2005, Volume 195, Issue 1, pp. 102 - 164

.... A few applications including the description of deformations of a scheme and equivariant deformations are considered...

Model category | Formal deformations | Presheaves of algebras | Dwyer–Kan localization | Dwyer-Kan localization | MATHEMATICS | Dwyer Kan localization | presheaves of algebras | COMPLEXES | formal deformations | model category | HOMOTOPY ALGEBRAS

Model category | Formal deformations | Presheaves of algebras | Dwyer–Kan localization | Dwyer-Kan localization | MATHEMATICS | Dwyer Kan localization | presheaves of algebras | COMPLEXES | formal deformations | model category | HOMOTOPY ALGEBRAS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2010, Volume 324, Issue 7, pp. 1483 - 1491

.... In the second section, consequences for the deformation theory of hom-algebras with surjective twisting map are discussed.

Nonassociative rings and algebras | Formal twistings | Nonstandard formal deformations | Hom-deformation theory | Hom-associative structures

Nonassociative rings and algebras | Formal twistings | Nonstandard formal deformations | Hom-deformation theory | Hom-associative structures

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2019, Volume 109, Issue 8, pp. 1747 - 1775

We explore extensions to (n)-Chern-Simons theory via the asymptotic properties of the Hitchin connection and its relation to Toeplitz operators developed previously by the first named author...

Geometric quantisation | Formal Hitchin-Witten connection | Complex Chern-Simons theory | KAHLER-MANIFOLDS | FIELD-THEORY | INVARIANTS | GEOMETRIC-QUANTIZATION | QUANTUM | PHYSICS, MATHEMATICAL | MODULAR FUNCTORS | DEFORMATION QUANTIZATION | TOEPLITZ QUANTIZATION | OPERATORS | Mathematics - Differential Geometry

Geometric quantisation | Formal Hitchin-Witten connection | Complex Chern-Simons theory | KAHLER-MANIFOLDS | FIELD-THEORY | INVARIANTS | GEOMETRIC-QUANTIZATION | QUANTUM | PHYSICS, MATHEMATICAL | MODULAR FUNCTORS | DEFORMATION QUANTIZATION | TOEPLITZ QUANTIZATION | OPERATORS | Mathematics - Differential Geometry

Journal Article

12.
Full Text
Mixed Hodge structures and representations of fundamental groups of algebraic varieties

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 869 - 910

Given a complex variety X, a linear algebraic group G and a representation ρ of the fundamental group π1(X,x) into G, we develop a framework for constructing a...

Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics

Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics

Journal Article

2006, 1. Aufl., Grundlehren der mathematischen Wissenschaften, ISBN 3540306080, Volume 334, xi, 339

.... Today deformation theory is highly formalized and has ramified widely. This self-contained account of deformation theory in classical algebraic geometry...

Schemes (Algebraic geometry) | Homotopy theory | Algebraic Geometry | Commutative Rings and Algebras | Mathematics

Schemes (Algebraic geometry) | Homotopy theory | Algebraic Geometry | Commutative Rings and Algebras | Mathematics

Book

Geometric and Functional Analysis, ISSN 1016-443X, 4/2008, Volume 18, Issue 1, pp. 184 - 221

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second...

Primary 14d05 | Secondary 32g05, 17b56 | differential graded Lie algebra | Hilbert scheme | Analysis | Formal deformation theory | Mathematics | Bernoulli number | Differential graded Lie algebra | MATHEMATICS | HOLOMORPHIC MAPS | CONNECTIONS | formal deformation theory

Primary 14d05 | Secondary 32g05, 17b56 | differential graded Lie algebra | Hilbert scheme | Analysis | Formal deformation theory | Mathematics | Bernoulli number | Differential graded Lie algebra | MATHEMATICS | HOLOMORPHIC MAPS | CONNECTIONS | formal deformation theory

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2016, Volume 445, pp. 78 - 102

...) through local homology. We discuss its basic properties and establish the basics results of a deformation theory, providing a characterization of smooth and étale morphisms...

Cotangent complex | Formal scheme | Local homology | Deformation | Lifting | MATHEMATICS | COMPLEX | ALGEBRAIC STACKS

Cotangent complex | Formal scheme | Local homology | Deformation | Lifting | MATHEMATICS | COMPLEX | ALGEBRAIC STACKS

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 108, Issue 9, pp. 2055 - 2097

.... As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 10/2020, Volume 224, Issue 10, p. 106382

... of elliptic cohomology theories. These orientations correspond to coordinates on deformations of formal groups that are compatible with norm maps along descent.

Complex orientation | Morava E-theory | Deformation of a formal group | Norm coherence | MATHEMATICS, APPLIED | FINITE SUBGROUPS | POWER OPERATIONS | ISOGENIES | GROUP LAWS | MATHEMATICS | COHOMOLOGY | ORIENTATION | SPECTRA

Complex orientation | Morava E-theory | Deformation of a formal group | Norm coherence | MATHEMATICS, APPLIED | FINITE SUBGROUPS | POWER OPERATIONS | ISOGENIES | GROUP LAWS | MATHEMATICS | COHOMOLOGY | ORIENTATION | SPECTRA

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 07/2004, Volume 69, Issue 1, pp. 223 - 235

In this Letter we give an overview on recent developments in representation theory of star product algebras...

Geometry | Morita equivalence | Deformation quantization | Mathematical and Computational Physics | Representation theory | Group Theory and Generalizations | Picard groupoid | Physics | Statistical Physics | FORMAL MORITA EQUIVALENCE | REPRESENTATIONS | deformation quantization | CONSTRUCTION | representation theory | STAR-PRODUCTS | PHYSICS, MATHEMATICAL

Geometry | Morita equivalence | Deformation quantization | Mathematical and Computational Physics | Representation theory | Group Theory and Generalizations | Picard groupoid | Physics | Statistical Physics | FORMAL MORITA EQUIVALENCE | REPRESENTATIONS | deformation quantization | CONSTRUCTION | representation theory | STAR-PRODUCTS | PHYSICS, MATHEMATICAL

Journal Article

Manuscripta Mathematica, ISSN 0025-2611, 11/2011, Volume 136, Issue 3, pp. 345 - 363

We study the sheaf T 1(X) of first order deformations of a reduced scheme with normal crossing singularities...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Algebraic Geometry | Mathematics, general | Mathematics | Number Theory | Primary 14D15 | 14D06 | THREEFOLDS | MATHEMATICS | SMOOTHINGS | RESOLUTION | FORMAL SCHEMES | SURFACES | 3-FOLDS

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Algebraic Geometry | Mathematics, general | Mathematics | Number Theory | Primary 14D15 | 14D06 | THREEFOLDS | MATHEMATICS | SMOOTHINGS | RESOLUTION | FORMAL SCHEMES | SURFACES | 3-FOLDS

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 8/2013, Volume 52, Issue 8, pp. 2910 - 2942

The paper has the form of a proposal concerned with the relationship between the three mathematically rigorous approaches to quantum field theory: (1...

Atiyah-Singer-Connes-Moscovici index | Deformation | Adiabatic limit | Fedosov’ formal index | Theoretical, Mathematical and Computational Physics | Quantum Physics | Microlocal renormalization | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Fedosov' formal index | SPECTRAL TRIPLES | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | QUANTUM | FIELD | GREENS FUNCTIONS | FORMULA | SUQ | IRREVERSIBLE-PROCESSES | RECIPROCAL RELATIONS | GEOMETRY | Analysis | Nuclear physics

Atiyah-Singer-Connes-Moscovici index | Deformation | Adiabatic limit | Fedosov’ formal index | Theoretical, Mathematical and Computational Physics | Quantum Physics | Microlocal renormalization | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Fedosov' formal index | SPECTRAL TRIPLES | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | QUANTUM | FIELD | GREENS FUNCTIONS | FORMULA | SUQ | IRREVERSIBLE-PROCESSES | RECIPROCAL RELATIONS | GEOMETRY | Analysis | Nuclear physics

Journal Article

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