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2013, Mathematical surveys and monographs, ISBN 9780821898468, Volume 189, xiii, 336
Book
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
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
Journal Article
数学学报:英文版, ISSN 1439-8516, 2015, Volume 31, Issue 10, pp. 1517 - 1530
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
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
Journal Article
Annals of Physics, ISSN 0003-4916, 12/2014, Volume 351, pp. 275 - 289
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
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
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
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
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
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
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
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
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
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
Journal Article
Forum Mathematicum, ISSN 0933-7741, 07/2019, Volume 31, Issue 4, pp. 867 - 905
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
Journal Article
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