Grôbner basis in the classification of characteristically nilpotent filiform Lie algebras of dimension 10

1996 ◽  
pp. 115-133
Author(s):  
F. J. Castro-Jiménez ◽  
J. Núñez-Valdés
Keyword(s):  
Lie Algebras ◽  
Gröbner Basis ◽  
Grobner Basis ◽  
Filiform Lie Algebras

scholarly journals Classification of Filiform Lie Algebras up to dimension 7 Over Finite Fields

2016 ◽  
Vol 24 (2) ◽  
pp. 185-204
Author(s):  
Óscar J. Falcón ◽  
Raúl M. Falcón ◽  
Juan Núñez ◽  
Ana M. Pacheco ◽  
M. Trinidad Villar
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Fields ◽  
Discrete Mathematics ◽  
Main Interest ◽  
Filiform Lie Algebras ◽  
Suitable Technique ◽  
New Strategies

Abstract This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie algebras up to dimension 7 over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomorphism, six, five and five 6-dimensional filiform Lie algebras and fifteen, eleven and fifteen 7-dimensional ones, respectively, over ℤ/pℤ, for p = 2, 3, 5. In any case, the main interest of the paper is not the computations itself but both to provide new strategies to find out properties of Lie algebras and to exemplify a suitable technique to be used in classifications for larger dimensions.

scholarly journals Classification of (n−5)-filiform Lie algebras

2001 ◽  
Vol 336 (1-3) ◽  
pp. 167-180 ◽  
Author(s):  
José Marı́a Ancochea Bermúdez ◽  
Otto Rutwig Campoamor Stursberg
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

scholarly journals Classification of filiform Lie algebras of order 3

2016 ◽  
Vol 110 ◽  
pp. 248-258
Author(s):  
Rosa María Navarro
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

New Results in the Classification of Filiform Lie Algebras

2016 ◽  
Vol 40 (1) ◽  
pp. 409-437 ◽  
Author(s):  
M. Ceballos ◽  
J. Núñez ◽  
Á. F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras

A DOMAIN TEST FOR LIE COLOR ALGEBRAS

2008 ◽  
Vol 07 (01) ◽  
pp. 81-90 ◽  
Author(s):  
KENNETH L. PRICE
Keyword(s):  
Lie Algebras ◽  
Gröbner Basis ◽  
Homogeneous Element ◽  
Ring Structure ◽  
Lie Superalgebras ◽  
Universal Enveloping Algebra ◽  
Grobner Basis ◽  
Graded Lie Algebras ◽  
Enveloping Algebra ◽  
Lie Color Algebras

Lie color algebras are generalizations of Lie superalgebras and graded Lie algebras. The properties of a Lie color algebra can often be related directly to the ring structure of its universal enveloping algebra. We study the effects of torsion elements and torsion subspaces. Let [Formula: see text] denote a Lie color algebra. If [Formula: see text] is homogeneous and torsion then x2 = 0 in [Formula: see text]. If no homogeneous element of [Formula: see text] is torsion, then [Formula: see text] so [Formula: see text] is semiprime. In this case we can give a test which uses Gröbner basis methods to determine when [Formula: see text] is a domain. This is applied in an example to show [Formula: see text] may be a domain even if [Formula: see text] contains torsion elements and torsion subspaces.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

Enhancing the extended hensel construction by using Gröbner basis

2017 ◽  
Vol 51 (1) ◽  
pp. 26-28
Author(s):  
Tateaki Sasaki ◽  
Daiju Inaba
Keyword(s):  
Gröbner Basis ◽  
Grobner Basis

scholarly journals Links among Characteristically Nilpotent, $C$-Graded and Derived Filiform Lie Algebras

2005 ◽  
Vol 35 (4) ◽  
pp. 1081-1098
Author(s):  
J.C. Benjumea ◽  
F.J. Echarte ◽  
M.C. Márquez ◽  
J. Núñez
Keyword(s):  
Lie Algebras ◽  
Filiform Lie Algebras
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