2013, Mathematical surveys and monographs, ISBN 9780821898468, Volume 189, xiii, 336

Book

2015, Volume 652.

Conference Proceeding

Journal of Algebra, ISSN 0021-8693, 11/2015, Volume 441, pp. 441 - 474

We classify group gradings on the simple Lie algebra L of type D 4 over an algebraically closed field of characteristic different from 2: fine gradings up to...

Composition algebra | Exceptional simple Jordan algebra | Simple Lie algebra | Triality | D 4 | Trialitarian algebra | Graded algebra | Cyclic composition algebra | Graded module | MATHEMATICS | FINE GRADINGS | D-4 | Algebra | Mathematics - Rings and Algebras

Composition algebra | Exceptional simple Jordan algebra | Simple Lie algebra | Triality | D 4 | Trialitarian algebra | Graded algebra | Cyclic composition algebra | Graded module | MATHEMATICS | FINE GRADINGS | D-4 | Algebra | Mathematics - Rings and Algebras

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

数学学报：英文版, ISSN 1439-8516, 2015, Volume 31, Issue 10, pp. 1517 - 1530

In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In...

Virasoro代数 | 导子代数 | 广义 | 自同构群 | 上同调群 | 李代数 | 结构理论 | 海森堡 | derivations | 17B68 | 17B40 | 17B65 | Mathematics, general | Mathematics | 2-cocycles | automorphisms | 17B05 | generalized Heisenberg–Virasoro algebras | Not-finitely graded Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | generalized Heisenberg-Virasoro algebras | 2ND COHOMOLOGY | Algebra | Studies | Theorems | Mathematical models | Derivation | Automorphisms | Group theory | Lie groups

Virasoro代数 | 导子代数 | 广义 | 自同构群 | 上同调群 | 李代数 | 结构理论 | 海森堡 | derivations | 17B68 | 17B40 | 17B65 | Mathematics, general | Mathematics | 2-cocycles | automorphisms | 17B05 | generalized Heisenberg–Virasoro algebras | Not-finitely graded Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | generalized Heisenberg-Virasoro algebras | 2ND COHOMOLOGY | Algebra | Studies | Theorems | Mathematical models | Derivation | Automorphisms | Group theory | Lie groups

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...

differential graded Lie algebras | Deformation of algebras | deformation complex | Hom-Lie-Rinehart algebras | MATHEMATICS | COHOMOLOGY | GERSTENHABER ALGEBRAS

differential graded Lie algebras | Deformation of algebras | deformation complex | Hom-Lie-Rinehart algebras | MATHEMATICS | COHOMOLOGY | GERSTENHABER ALGEBRAS

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

Annals of Physics, ISSN 0003-4916, 12/2014, Volume 351, pp. 275 - 289

We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what...

Quantum relativity | Lie algebra contractions | Relativity symmetry | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | CONTINUOUS GRADED CONTRACTIONS | DISCRETE | DEFORMATIONS | VARIABLES | SO(N+1) | SEPARATION | Algebra | Physics | Lie groups | Pictures | Kinematics | Relativity | Representations | Arenas | Preserving | Symmetry | RELATIVITY THEORY | SPACE-TIME | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | LIE GROUPS

Quantum relativity | Lie algebra contractions | Relativity symmetry | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | CONTINUOUS GRADED CONTRACTIONS | DISCRETE | DEFORMATIONS | VARIABLES | SO(N+1) | SEPARATION | Algebra | Physics | Lie groups | Pictures | Kinematics | Relativity | Representations | Arenas | Preserving | Symmetry | RELATIVITY THEORY | SPACE-TIME | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | LIE GROUPS

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2017, Volume 473, pp. 29 - 65

Let (g0,B0) be a quadratic Lie algebra (i.e. a Lie algebra g0 with a non-degenerate symmetric invariant bilinear form B0) and let (ρ,V) be a finite dimensional...

Graded Lie Algebras | Representations | Quadratic Lie algebras | Reductive Lie algebras | MATHEMATICS | INVARIANT | Algebra | Mathematics | Representation Theory

Graded Lie Algebras | Representations | Quadratic Lie algebras | Reductive Lie algebras | MATHEMATICS | INVARIANT | Algebra | Mathematics | Representation Theory

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 17, pp. 7195 - 7201

The study of contractions of Lie algebras is profusely extended in the last decades. In this paper we study the graded contractions of some lower‐dimensional...

contractions of algebras | filiform Lie algebras | graded contractions | MATHEMATICS, APPLIED | Algebra | Lie groups

contractions of algebras | filiform Lie algebras | graded contractions | MATHEMATICS, APPLIED | Algebra | Lie groups

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

Journal of Algebra, ISSN 0021-8693, 11/2015, Volume 441, pp. 441 - 474

We classify group gradings on the simple Lie algebra L of type D4 over an algebraically closed field of characteristic different from 2: fine gradings up to...

Composition algebra | Exceptional simple Jordan algebra | Simple Lie algebra | Triality | formula omitted | Trialitarian algebra | Graded algebra | Cyclic composition algebra | Graded module

Composition algebra | Exceptional simple Jordan algebra | Simple Lie algebra | Triality | formula omitted | Trialitarian algebra | Graded algebra | Cyclic composition algebra | Graded module

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

Journal of Algebra, ISSN 0021-8693, 07/2018, Volume 506, pp. 1 - 42

For any abelian group G, we classify up to isomorphism all G-gradings on the classical central simple Lie algebras, except those of type D4, over the field of...

Classical simple Lie algebra | Real algebra | Graded algebra | Graded module | Classification | MATHEMATICS | FINE GRADINGS | Algebra | Mathematics - Rings and Algebras

Classical simple Lie algebra | Real algebra | Graded algebra | Graded module | Classification | MATHEMATICS | FINE GRADINGS | Algebra | Mathematics - Rings and Algebras

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2014, Volume 55, Issue 1, p. 11701

We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽...

PHYSICS, MATHEMATICAL | SUPERGRAVITY THEORY | Supersymmetry | Tensors | Algebra | Mathematical analysis | Deformation mechanisms | Lie groups | Embedding | Decomposition | Representations | Supergravity | Quantum theory | TENSORS | SUPERGRAVITY | SUPERSYMMETRY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | DUALITY | GRADED LIE GROUPS | DEFORMATION

PHYSICS, MATHEMATICAL | SUPERGRAVITY THEORY | Supersymmetry | Tensors | Algebra | Mathematical analysis | Deformation mechanisms | Lie groups | Embedding | Decomposition | Representations | Supergravity | Quantum theory | TENSORS | SUPERGRAVITY | SUPERSYMMETRY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | DUALITY | GRADED LIE GROUPS | DEFORMATION

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2017, Volume 477, pp. 294 - 311

The algebras UTn of the n×n upper triangular matrices over a field K are of significant importance in the theory of algebras with polynomial identities. Group...

Gradings on Lie algebras | Elementary gradings | Group graded algebras | Upper triangular matrices | MATHEMATICS | JORDAN | IDENTITIES | Algebra

Gradings on Lie algebras | Elementary gradings | Group graded algebras | Upper triangular matrices | MATHEMATICS | JORDAN | IDENTITIES | Algebra

Journal Article

JOURNAL OF ALGEBRA, ISSN 0021-8693, 04/2015, Volume 427, pp. 226 - 251

Let K be a field of characteristic 0 and let W-1 be the Lie algebra of the derivations of the polynomial ring K[t]. The algebra W-1 admits a natural Z-grading....

MATHEMATICS | Graded T-ideal | Graded Lie algebra | SL | Infinite basis of graded identities | Graded identities | Basis of identities | POLYNOMIAL-IDENTITIES | Algebra

MATHEMATICS | Graded T-ideal | Graded Lie algebra | SL | Infinite basis of graded identities | Graded identities | Basis of identities | POLYNOMIAL-IDENTITIES | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 2010, Volume 324, Issue 12, pp. 3532 - 3571

The fine abelian group gradings on the simple classical Lie algebras (including D 4 ) over algebraically closed fields of characteristic 0 are determined up to...

Graded division algebra | Fine | Grading | Lie algebra | Simple | MATHEMATICS | ASSOCIATIVE ALGEBRAS | TRIALITY

Graded division algebra | Fine | Grading | Lie algebra | Simple | MATHEMATICS | ASSOCIATIVE ALGEBRAS | TRIALITY

Journal Article

Forum Mathematicum, ISSN 0933-7741, 07/2019, Volume 31, Issue 4, pp. 867 - 905

We explore the graded-formality and filtered-formality properties of finitely generated groups by studying the various Lie algebras over a field of...

Chen Lie algebra | Malcev Lie algebra | 1-formality | 20J05 | holonomy Lie algebra | 16W70 | 55P62 | Seifert manifold | filtered-formality | 20F40 | 57M05 | graded-formality | 20F18 | nilpotent group | 17B70 | minimal model | Central series | 20F14 | 16S37 | TOPOLOGY | MATHEMATICS, APPLIED | SPACES | CUP PRODUCTS | LOWER CENTRAL SERIES | PRESENTATIONS | NILMANIFOLDS | MATHEMATICS | COMPLETION | RATIONAL HOMOTOPY-THEORY | HOMOLOGY | GEOMETRY | Algebra | Fields (mathematics) | Quotients | Group theory | Lie groups

Chen Lie algebra | Malcev Lie algebra | 1-formality | 20J05 | holonomy Lie algebra | 16W70 | 55P62 | Seifert manifold | filtered-formality | 20F40 | 57M05 | graded-formality | 20F18 | nilpotent group | 17B70 | minimal model | Central series | 20F14 | 16S37 | TOPOLOGY | MATHEMATICS, APPLIED | SPACES | CUP PRODUCTS | LOWER CENTRAL SERIES | PRESENTATIONS | NILMANIFOLDS | MATHEMATICS | COMPLETION | RATIONAL HOMOTOPY-THEORY | HOMOLOGY | GEOMETRY | Algebra | Fields (mathematics) | Quotients | Group theory | Lie groups

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2018, Volume 512, pp. 382 - 426

We classify group gradings on the simple Lie algebras of types G2 and D4 over the field of real numbers (or any real closed field): fine gradings up to...

Composition algebra | Triality | Twisted composition | Trialitarian algebra | Graded algebra | Real simple Lie algebra | Cyclic composition

Composition algebra | Triality | Twisted composition | Trialitarian algebra | Graded algebra | Real simple Lie algebra | Cyclic composition

Journal Article

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