Doklady Mathematics, ISSN 1064-5624, 11/2018, Volume 98, Issue 3, pp. 626 - 628

The present paper is devoted to the classification of infinite-dimensional naturally graded Lie algebras that are narrow in the sense of Zelmanov and Shalev...

Mathematics, general | Mathematics | MATHEMATICS

Mathematics, general | Mathematics | MATHEMATICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2016, Volume 466, pp. 229 - 283

The Grigorchuk and Gupta–Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic...

Restricted Lie algebras | Nil-algebras | Growth | p-groups | Graded algebras | Lie algebras of differential operators | Self-similar algebras | Lie superalgebra | GRADINGS | RINGS | EXAMPLES | SUBALGEBRAS | MATHEMATICS | ASSOCIATIVE ALGEBRAS | Algebra

Restricted Lie algebras | Nil-algebras | Growth | p-groups | Graded algebras | Lie algebras of differential operators | Self-similar algebras | Lie superalgebra | GRADINGS | RINGS | EXAMPLES | SUBALGEBRAS | MATHEMATICS | ASSOCIATIVE ALGEBRAS | Algebra

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850069

We construct three families of vertex algebras along with their modules from appropriate vertex Lie algebras, using the constructions in [Vertex Lie algebra,...

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Journal Article

Compositio Mathematica, ISSN 0010-437X, 08/2015, Volume 151, Issue 8, pp. 1499 - 1528

To study infinitesimal deformation problems with cohomology constraints, we introduce and study cohomology jump functors for differential graded Lie algebra...

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry

Journal Article

UNIVERSE, ISSN 2218-1997, 12/2018, Volume 4, Issue 12, p. 138

We propose the notion of (q, sigma, tau)-differential graded algebra, which generalizes the notions of (sigma, tau)-differential graded algebra and...

LIE-ALGEBRAS | pre-cosimplicial complex | VIRASORO ALGEBRA | ASTRONOMY & ASTROPHYSICS | q-differential graded algebra | (sigma, tau)-differential graded algebra | generalized Clifford algebra | PHYSICS, PARTICLES & FIELDS | (σ, τ)-differential graded algebra

LIE-ALGEBRAS | pre-cosimplicial complex | VIRASORO ALGEBRA | ASTRONOMY & ASTROPHYSICS | q-differential graded algebra | (sigma, tau)-differential graded algebra | generalized Clifford algebra | PHYSICS, PARTICLES & FIELDS | (σ, τ)-differential graded algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 04/2020, Volume 48, Issue 4, pp. 1653 - 1670

We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using...

17B55 | 17B99 | differential graded Lie algebras | 17A30 | Deformation of algebras | deformation complex | Hom-Lie-Rinehart algebras

17B55 | 17B99 | differential graded Lie algebras | 17A30 | Deformation of algebras | deformation complex | Hom-Lie-Rinehart algebras

Journal Article

Hokkaido Mathematical Journal, ISSN 0385-4035, 2018, Volume 47, Issue 3, pp. 445 - 464

In this paper, we provide a new invariant for partial differential equations (PDEs) under contact transformations by using nilpotent graded Lie algebras. By...

Nilpotent graded Lie algebras | (Linear) differential systems | Invariant of differential equations | MATHEMATICS | PLANE

Nilpotent graded Lie algebras | (Linear) differential systems | Invariant of differential equations | MATHEMATICS | PLANE

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2012, Volume 62, Issue 12, pp. 2389 - 2400

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected. We...

Hypercrossed complex | Dg Lie algebra | Simplicial Lie algebra | 1-jet | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | HOMOTOPY THEORY | GEOMETRY | Algebra

Hypercrossed complex | Dg Lie algebra | Simplicial Lie algebra | 1-jet | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | HOMOTOPY THEORY | GEOMETRY | Algebra

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 05/2016, Volume 33, Issue 12, p. 125033

We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano...

QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | conformal Killing-Yano forms | ASTRONOMY & ASTROPHYSICS | CURRENTS | graded Lie algebra | SPINORS | constant curvature manifolds | Einstein manifolds | PHYSICS, PARTICLES & FIELDS

QUANTUM SCIENCE & TECHNOLOGY | PHYSICS, MULTIDISCIPLINARY | conformal Killing-Yano forms | ASTRONOMY & ASTROPHYSICS | CURRENTS | graded Lie algebra | SPINORS | constant curvature manifolds | Einstein manifolds | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Algebra, ISSN 0021-8693, 06/2018, Volume 504, pp. 291 - 335

The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic...

Restricted Lie algebras | Finite width | Lie superalgebras | Nil-algebras | Growth | Fractal algebras | Graded algebras | Lie algebras of differential operators | Self-similar algebras | Linear growth | Thin Lie algebras | Just infinite | Filiform Lie algebras | Gelfand–Kirillov dimension

Restricted Lie algebras | Finite width | Lie superalgebras | Nil-algebras | Growth | Fractal algebras | Graded algebras | Lie algebras of differential operators | Self-similar algebras | Linear growth | Thin Lie algebras | Just infinite | Filiform Lie algebras | Gelfand–Kirillov dimension

Journal Article

Communications in Algebra, ISSN 0092-7872, 07/2017, Volume 45, Issue 7, pp. 2912 - 2941

The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic...

16S32 | Divided power algebra | 16N40 | Lie algebras of differential operators | 16P90 | Lie superalgebra | self-similar algebras | 17B66 | restricted Lie algebras | 17B65 | 17B70 | growth | 17B50 | nil-algebras | graded algebras | MATHEMATICS | EXAMPLES | Integers | Algebra | Group theory | Lie groups | Mapping | Generators | Hulls (structures) | Hulls | Self-similarity | Associative | Derivation | Polynomials

16S32 | Divided power algebra | 16N40 | Lie algebras of differential operators | 16P90 | Lie superalgebra | self-similar algebras | 17B66 | restricted Lie algebras | 17B65 | 17B70 | growth | 17B50 | nil-algebras | graded algebras | MATHEMATICS | EXAMPLES | Integers | Algebra | Group theory | Lie groups | Mapping | Generators | Hulls (structures) | Hulls | Self-similarity | Associative | Derivation | Polynomials

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2012, Volume 6, Issue 2, pp. 343 - 387

We introduce the new notion of epsilon-graded associative algebras which takes its roots from the notion of commutation factors introduced in the context of...

ε-graded associative algebra | Derivation-based differential calculus | ε-derivations and connections | MATHEMATICS, APPLIED | FIELD-THEORY | CALCULUS | DIFFERENTIAL GEOMETRY | PHYSICS, MATHEMATICAL | DERIVATIONS | INDUCED GAUGE-THEORY | LIE-ALGEBRAS | MATHEMATICS | epsilon-derivations | epsilon-graded associative algebra | SPACE QUANTUM-MECHANICS | MATRIX ALGEBRAS | connections

ε-graded associative algebra | Derivation-based differential calculus | ε-derivations and connections | MATHEMATICS, APPLIED | FIELD-THEORY | CALCULUS | DIFFERENTIAL GEOMETRY | PHYSICS, MATHEMATICAL | DERIVATIONS | INDUCED GAUGE-THEORY | LIE-ALGEBRAS | MATHEMATICS | epsilon-derivations | epsilon-graded associative algebra | SPACE QUANTUM-MECHANICS | MATRIX ALGEBRAS | connections

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2012, Volume 14, Issue 2, pp. 521 - 540

We use the Thom-Whitney construction to show that infinitesimal deformations of a coherent sheaf F are controlled by the differential graded Lie algebra of...

Differential graded Lie algebras | Functors of Artin rings | MATHEMATICS | MATHEMATICS, APPLIED | functors of Artin rings

Differential graded Lie algebras | Functors of Artin rings | MATHEMATICS | MATHEMATICS, APPLIED | functors of Artin rings

Journal Article

Journal of Algebra, ISSN 0021-8693, 09/2015, Volume 438, pp. 90 - 118

We give some formality criteria for a differential graded Lie algebra to be formal. For instance, we show that a DG-Lie algebra L is formal if and only if the...

Differential graded Lie algebras | [formula omitted]-algebras | Spectral sequences | L ∞ -algebras | KAHLER-MANIFOLDS | MATHEMATICS | MODELS | SPACES | OBSTRUCTIONS | L-infinity-algebras | HOMOTOPY-THEORY | DEFORMATION-THEORY | MODULI | Algebra

Differential graded Lie algebras | [formula omitted]-algebras | Spectral sequences | L ∞ -algebras | KAHLER-MANIFOLDS | MATHEMATICS | MODELS | SPACES | OBSTRUCTIONS | L-infinity-algebras | HOMOTOPY-THEORY | DEFORMATION-THEORY | MODULI | Algebra

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 05/2016, Volume 27, Issue 5, p. 1650046

We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along...

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | 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 Zhejiang University, Science Edition, ISSN 1008-9497, 05/2016, Volume 43, Issue 3, pp. 253 - 263

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 10/2018, Volume 21, Issue 5, pp. 1037 - 1069

We discuss the notion of characteristic Lie algebra of a hyperbolic PDE. The integrability of a hyperbolic PDE is closely related to the properties of the...

Tzitzeica equation | Bell polynomial | Kac-Moody algebra | Hyperbolic PDE | Sine-Gordon equation | Naturally graded Lie algebra | Loop algebra | Characteristic Lie algebra | Gelfand-Kirillov dimension | INTEGRABILITY | DIFFERENTIAL-EQUATIONS | CLASSIFICATION | MATHEMATICS | NON-LINEAR SYSTEM | DYNAMICAL-SYSTEMS | Algebra

Tzitzeica equation | Bell polynomial | Kac-Moody algebra | Hyperbolic PDE | Sine-Gordon equation | Naturally graded Lie algebra | Loop algebra | Characteristic Lie algebra | Gelfand-Kirillov dimension | INTEGRABILITY | DIFFERENTIAL-EQUATIONS | CLASSIFICATION | MATHEMATICS | NON-LINEAR SYSTEM | DYNAMICAL-SYSTEMS | Algebra

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 08/2017, Volume 80, Issue 1, pp. 115 - 142

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality:...

graded bundle | homogeneity structure | Zakrzewski morphism | duality | N-manifold | LIE ALGEBROIDS | PHYSICS, MATHEMATICAL | VECTOR-BUNDLES | Algebra

graded bundle | homogeneity structure | Zakrzewski morphism | duality | N-manifold | LIE ALGEBROIDS | PHYSICS, MATHEMATICAL | VECTOR-BUNDLES | Algebra

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2012, Volume 8, p. 038

In this paper we first state the classification of the prolongations of complex free fundamental graded Lie algebras. Next we introduce the notion of free...

Fundamental graded lie algebra | Prolongation | Pseudo-product graded lie algebra | prolongation | fundamental graded Lie algebra | PHYSICS, MATHEMATICAL | pseudo-product graded Lie algebra

Fundamental graded lie algebra | Prolongation | Pseudo-product graded lie algebra | prolongation | fundamental graded Lie algebra | PHYSICS, MATHEMATICAL | pseudo-product graded Lie algebra

Journal Article

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