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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 Pure and Applied Algebra, ISSN 0022-4049, 01/2019, Volume 223, Issue 1, pp. 349 - 368
We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form g⊗FF[t1,…,tℓ]/I, where g is a finite-dimensional Lie... 
LIE-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | RINGS | EQUIVARIANT MAP ALGEBRAS | WEYL MODULES | Algebra
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 10/2017, Volume 20, Issue 5, pp. 1085 - 1107
For any grading by an abelian group G on the exceptional simple Lie algebra ℒ $\mathcal {L}$ of type E 6 or E 7 over an algebraically closed field of... 
Primary 16W50 | Non-associative Rings and Algebras | Commutative Rings and Algebras | Mathematics | Simple | Graded | Secondary 17B70 | Associative Rings and Algebras | 17B25 | Graded Brauer invariant | 17B60 | Module | Exceptional Lie algebra | MATHEMATICS | FINE GRADINGS | Algebra
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1249 - 1276
We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings $$\mathfrak {f}_{c,d}$$ fc,d of... 
Graded ideal zeta functions | Local functional equations | Free nilpotent Lie rings | 11M41 | 11S40 | Mathematics, general | 17B70 | Mathematics | MATHEMATICS | ALGEBRAS | ZETA-FUNCTIONS | SUBGROUPS
Journal Article
Communications in Algebra, ISSN 0092-7872, 10/2018, Volume 46, Issue 10, pp. 4187 - 4200
A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a... 
Lie color algebra | graded algebra | structure theory | Gerstenhaber algebra | Poisson algebra | Schouten algebra | simple component | 17B63 | 17B20 | 17B75 | 17B70 | 17B05 | MATHEMATICS | GEOMETRY
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2017, Volume 2017, Issue 723, pp. 153 - 215
The infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when... 
MATHEMATICS | SPACES | SYSTEMS | Mathematics - Differential Geometry | VDP | parabolic geometry | Submaximal symmetry | harmonic curvature | Tanaka theory | Matematikk og Naturvitenskap: 400 | Mathematics and natural science: 400 | Mathematics: 410 | Matematikk: 410
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 10/2018, Volume 13, Issue 5, pp. 1179 - 1187
Let $$\mathfrak{g} = W_1 $$ g = W 1 be the Witt algebra over an algebraically closed field k of characteristic p > 3; and let be the commuting variety of g. In... 
irreducible component | Witt algebra | Mathematics, general | 17B70 | Mathematics | 17B50 | commuting variety | dimension | 17B05 | LIE-ALGEBRAS | MATHEMATICS | Mathematical analysis | Algebra | Lie groups
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2019, Volume 517, pp. 249 - 275
We classify finite dimensional Hm2(ζ)-simple Hm2(ζ)-module Lie algebras L over an algebraically closed field of characteristic 0 where Hm2(ζ) is the mth Taft... 
PI-exponent | Codimension | Taft algebra | Lie algebra | H-module algebra | Polynomial identity | MATHEMATICS | IDENTITIES | GROWTH | Algebra
Journal Article
Forum Mathematicum, ISSN 0933-7741, 01/2016, Volume 28, Issue 1, pp. 101 - 128
We motivate and study the reduced Koszul map, relating the invariant bilinear maps on a Lie algebra and the third homology. We show that it is concentrated in... 
17B55 | 17B56 | 15A63 | 17B30 | 17B70 | 19C09 | nilpotent Lie algebra | Lie algebra homology | current Lie algebra | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | CENTRAL EXTENSIONS | INVARIANT | HOMOLOGY
Journal Article
Canadian Journal of Mathematics, ISSN 0008-414X, 08/2017, Volume 69, Issue 4, pp. 721 - 766
Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we introduce and study Kantor pairs with short Peirce gradings and relate... 
Graded Lie algebra | Kantor pair | Jordan pair | LIE-ALGEBRAS | MATHEMATICS | graded Lie algebra | TRIPLE-SYSTEMS | Mathematics - Rings and Algebras
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 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
Archiv der Mathematik, ISSN 0003-889X, 5/2016, Volume 106, Issue 5, pp. 431 - 438
We discuss the notion of singular formal deformation in algebraic setup. Such deformations show up in both finite and infinite dimensional structures. It turns... 
16E40 | 17B55 | Formal deformation | Mathematics, general | 17B70 | Singular deformation | Mathematics | 16S80 | 13D10 | 14B12 | Lie algebra | 14D15 | Algebra
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 09/2019, Volume 110, pp. 197 - 234
The group of basis-conjugating automorphisms of the free group of rank n, also known as the McCool group or the welded braid group PΣn, contains a much-studied... 
Resonance varieties | Resonance scheme | McCool and upper McCool groups | Chen ranks | Infinitesimal Alexander invariant | MATHEMATICS, APPLIED | COHOMOLOGY | BRAID | INVARIANTS | LOWER CENTRAL SERIES | AUTOMORPHISMS
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2015, Volume 105, Issue 12, pp. 1703 - 1723
We study integrable non-degenerate Monge–Ampère equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded... 
37K25 | Petrov type | conformal structure | Lax pair | Monge–Ampère equation | Theoretical, Mathematical and Computational Physics | 76M60 | hyper-Hermitian | Statistical Physics, Dynamical Systems and Complexity | self-duality | Physics | Geometry | 17B65 | integrable deformation | 17B80 | 17B70 | Group Theory and Generalizations | recursion operator | Algebra
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 4/2018, Volume 41, Issue 2, pp. 637 - 656
In this paper, we give some properties of the generalized derivation algebra $$\mathrm{GDer}(T)$$ GDer(T) of a Hom–Lie triple systems T. In particular, we... 
17A75 | 17B30 | Hom–Lie triple systems | Mathematics, general | Generalized derivations | 17B70 | Mathematics | Centroids | Applications of Mathematics | MATHEMATICS | ALGEBRAS | COHOMOLOGY | Hom-Lie triple systems | EXTENSIONS | NAMBU | DEFORMATIONS | SUPERALGEBRAS | Embedded systems
Journal Article
Publ. Mat, 2016, Volume 60, Issue no. 1, pp. 113 - 170
There are fourteen fine gradings on the exceptional Lie algebra \mathfrak e_6 over an algebraically closed field of zero characteristic. We provide their... 
exceptional Lie algebra | maximal abelian diagonalizable group | 17B70 | 17B25 | Graded algebra
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 09/2009, Volume 46, Issue 3, pp. 611 - 643
We study the subalgebra of fixed points of a root graded Lie algebra under a certain class of finite order automorphisms. As the centerless core of extended... 
MATHEMATICS | SYSTEMS | 17B40 | 17B67 | 17B70
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2019, Volume 42, Issue 4, pp. 1567 - 1606
In this paper, we study Rota–Baxter operators and super $$\mathcal {O}$$ O -operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and... 
Associative superalgebra | 17A36 | L -dendriform superalgebras | 17A30 | Pre-Lie superalgebra | Mathematics, general | 17B70 | Mathematics | Rota–Baxter operator | Applications of Mathematics | Super $$\mathcal {O}$$ O -operator | Lie superalgebra | L-dendriform superalgebras | Super O-operator | MATHEMATICS | Rota-Baxter operator | ALGEBRAIC APPROACH | O-OPERATORS | Operators
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2019, Volume 202, Issue 1, pp. 233 - 264
We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $$J:{{\mathrm{\mathrm... 
Lie algebra isomorphism | Scalar product | Mathematics | Topology | Pseudo H -type Lie algebras | 22E15 | Involution | Primary 17B60 | 17B30 | Convex and Discrete Geometry | Nilpotent 2-step Lie algebra | Clifford module | Algebraic Geometry | 17B70 | Hyperbolic Geometry | Projective Geometry | Differential Geometry | Pseudo H-type Lie algebras | MATHEMATICS | SYMMETRIC-SPACES | LATTICES
Journal Article
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