The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
Non-Existence of Complex Structures on Filiform Lie Algebras
[article]

2003
*
arXiv
*
pre-print

The aim

arXiv:math/0103035v2
fatcat:plmqd6jbcne3vhoi2vwyuie26q
*of*this work is to prove the nonexistence*of**complex*structures over nilpotent*Lie**algebras**of*maximal class (also called*filiform*). ... Then no 2n−*dimensional**complex**filiform**Lie**algebra*is a vectorial direct sum*of*two n−*dimension**filiform*sub-*algebras*. Proof. ... Thus g 1 or σ(g 1 ) is a n−*dimensional**complex**filiform**Lie**algebra*. ...##
###
Links among Characteristically Nilpotent, $C$-Graded and Derived Filiform Lie Algebras

2005
*
Rocky Mountain Journal of Mathematics
*

At the same time we offer an algorithm that will allow us to know, given a

doi:10.1216/rmjm/1181069676
fatcat:jg2ujpxm5jakporp6qjlwbdhla
*complex**filiform**Lie**algebra*, which*of*those properties hold. ... The aim*of*this paper is to study the interconnectivity among*Lie**algebras*that are characteristically nilpotent, derived and c-graded*filiform*, establishing some characterization theorems involving them ... It was used by Ancochea and Goze to classify*complex*nilpotent*Lie**algebras**of**dimension*7 and*complex**filiform**Lie**algebras**of**dimension*8, since it is an invariant*of*these*algebras*, in the sense*of*...##
###
Page 1861 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

We find that there exist 188 families

*of**complex**filiform**Lie**algebras**of**dimension**11*.” Athanassios I. ... Summary: “In this paper we give the explicit classification*of**complex**filiform**Lie**algebras**of**dimension**11*. ...##
###
An algorithm to obtain laws of families of filiform Lie algebras

1998
*
Linear Algebra and its Applications
*

By this recursive algorithm, we obtain parametrizations

doi:10.1016/s0024-3795(97)10077-5
fatcat:hyy3r65ndjhirpvng6isbnw22u
*of*the affine*algebraic*sets*of**filiform**Lie**algebras**of**dimensions**11*and 12. 0 1998 Elsevier Science Inc. All rights reserved. ... We present a polynomial time algorithm which generates families*of**filiform**Lie**algebras**of**dimension*n. ... It allows to deal with the variety in a easier way. 0 The laws*of**filiform**Lie**algebras**of**dimensions**11*and 12 In this section we consider the set*of*laws*of**filiform**Lie**algebras**of**dimensions**11*and ...##
###
Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine

2015
*
Symmetry
*

This paper addresses the problem

doi:10.3390/sym7041788
fatcat:4gqgq5w4ojhltcfrupjdcgsn3a
*of*computing the family*of*two-*filiform**Lie**algebra*laws*of**dimension*nine using three*Lie**algebra*properties converted into matrix form properties: Jacobi identity, nilpotence ... This structure theorem permits the exhaustive classification*of*the quasi-*filiform*nilpotent*Lie**algebras**of**dimension*nine with current computational methodologies. ... López from University*of*Sevilla for their support and orientation on the knowledge*of**Lie**Algebras*. ...##
###
Invariant functions and contractions of certain types of Lie algebras of lower dimensions

2018
*
Journal of Nonlinear Mathematical Physics
*

We focus the study

doi:10.1080/14029251.2018.1494705
fatcat:zvfvlwipx5ebldax6unqcmeoay
*of*these functions in the frame*of*the*filiform**Lie**algebras*, trying to extend to these*algebras*some*of*the properties*of*such functions over semi-simple*Lie**algebras*. ... In this paper, we deal with contractions*of**Lie**algebras*. ... Indeed, although by using a different procedure, we have confirmed some results by those authors and have also obtained new results in the case*of**filiform**Lie**algebras**of**dimension*5. ...##
###
Low-dimensional filiform Lie algebras

1998
*
Journal of Pure and Applied Algebra
*

We give a complete classification up to isomorphisms

doi:10.1016/s0022-4049(97)00096-0
fatcat:kgb6hgywbfeh7gkd2x2eg2x7tu
*of**complex**filiform**Lie**algebras**of**dimension*m with M 5*11*. ... IYk"r(Xk,Xk+l) =x" &,u" E ~2('%,-bz)~ Let 5% be the variety*of**filiform**Lie**algebras*laws in a m-*dimensional*vectorial space. ...*Filiform**Lie**algebras**of**dimension*m 5*11*In this section we present the classes*of**filiform**Lie**algebras*laws*of**dimension**11*or less which are classified in the sections below. ...##
###
Characteristically nilpotent Lie algebras and symplectic structures
[article]

2004
*
arXiv
*
pre-print

Among these

arXiv:math/0409251v1
fatcat:ay56ubzyi5fudj6zq7gwged2ca
*Lie**algebras*are*filiform*CNLAs*of**dimension*n< 14. It turns out that there are many examples*of*CNLAs which admit a symplectic structure. ... A generalization*of*a sympletic structure is an affine structure on a*Lie**algebra*. ... All*complex**Lie**algebras**of**dimension*n ≤ 4 are affine except for sl 2 (C), and all*complex*nilpotent*Lie**algebras**of**dimension*n ≤ 7 are affine. ...##
###
A class of nilpotent lie algebras

2000
*
Communications in Algebra
*

A pfiliform

doi:10.1080/00927870008827102
fatcat:ky3ddyjprbgadf2zwwqxxk4m4q
*Lie**algebra*g is a nilpotent*Lie**algebra*for which Goze's invariant is (np, 1,. . . , I ) . These*Lie**algebras*are well known for p 2 n -4, n = dirn(g). ... In this paper we describe the pfiliform*Lie**algebras*, for p = n -5 and we give their classification when the derived subalgebra is maximal. ... ACKNOWLEDGEMENTS This work was partly supported by the PAICYT, FQM143*of*the Junta de Andalucia (Spain) and project UPV 066.163-EA032/98*of*Univ. Pals Vasco (Spain). ...##
###
Characteristically nilpotent Lie algebras and symplectic structures

2006
*
Forum mathematicum
*

Among these

doi:10.1515/forum.2006.038
fatcat:sf4s5hgivbdjdkw2xyeg6kiebu
*Lie**algebras*are*filiform*CNLAs*of**dimension*n ≤ 14. It turns out that there are many examples*of*CNLAs which admit a symplectic structure. ... A generalization*of*a sympletic structure is an affine structure on a*Lie**algebra*. ... Every 10-*dimensional**complex*symplectic*filiform**Lie**algebra*is isomorphic to one*of*the following laws: µ 9 10 (α), µ 10 10 , µ*11*10 , µ 13 10 (α, β), µ 16 10 (α, β), µ 26 10 (0, β), µ 27 10 , µ 29 10 ...##
###
On filiform Lie algebras. Geometric and algebraic studies
[article]

2017
*
arXiv
*
pre-print

A finite

arXiv:1712.00318v1
fatcat:3ohecpyaljesnlkuxdt47p6j7y
*dimensional**filiform*K-*Lie**algebra*is a nilpotent*Lie**algebra*g whose nil index is maximal, that is equal to dim g -1. ... If we fix a Vergne's basis, the set*of**filiform*n-*dimensional**Lie**algebras*is a closed Zariski subset*of*an affine space generated by the structure constants associated with this fixed basis. ... We do the same thing for the*dimensions*10 and*11*, giving the description*of*the contact*11*-*dimensional**filiform**Lie**algebras*and consequently the description*of*the symplectic 10-*dimensional**filiform*...##
###
Graded filiform Lie algebras and symplectic nilmanifolds
[article]

2002
*
arXiv
*
pre-print

It is proved that a symplectic

arXiv:math/0205042v1
fatcat:wsdfdb2ltnhf5hsemnhu2sebem
*filiform**Lie**algebra*is a filtered deformation*of*some N-graded symplectic*filiform**Lie**algebra*. But this condition is not sufficient. ... In particular we describe the spaces*of*symplectic cohomology classes for all even-*dimensional**algebras**of*the list. ... Acknowledgments This work started from discussions on results*of*[19] , [20] , [24] with S. Salamon during the visit to the Torino University in December 2000. The author is very grateful to A. ...##
###
Filiform Lie algebras of dimension 8 as degenerations
[article]

2013
*
arXiv
*
pre-print

For each

arXiv:1308.4580v1
fatcat:vk5jg7kv6ng4fboivsiy24r2hm
*complex*8-*dimensional**filiform**Lie**algebra*we find another non isomorphic*Lie**algebra*that degenerates to it. ... Since this is already known for nilpotent*Lie**algebras**of*rank > 1, only the caracteristically nilpotent ones should be considered. ... This paper is part*of*the PhD. thesis*of*the first author. He thanks CONICET for the Ph.D. fellowship awarded that made this possible. ...##
###
On nilpotent filiform Lie algebras of dimension eight

2003
*
International Journal of Mathematics and Mathematical Sciences
*

The aim

doi:10.1155/s016117120311201x
fatcat:j4yvn7t3zzdedkaxdc7w3aldx4
*of*this paper is to determine both the Zariski constructible set*of*characteristically nilpotent*filiform**Lie*algebrasgof dimension8and that*of*the set*of*nilpotent*filiform**Lie**algebras*whose ... group*of*automorphisms consists*of*unipotent automorphisms, in the variety*of**filiform**Lie**algebras**of*dimension8overC. ... Consider the set*of**complex**filiform**Lie**algebras*. Consider C 8 with ...##
###
There are no rigid filiform Lie algebras of low dimension
[article]

2017
*
arXiv
*
pre-print

We prove that there are no rigid

arXiv:1709.04793v1
fatcat:yjajr4j5bbhfnkplwc6prgf6r4
*complex**filiform**Lie**algebras*in the variety*of*(*filiform*)*Lie**algebras**of**dimension*less than or equal to*11*. ... This follows by constructing non trivial linear deformations in a Zariski open dense set*of*the variety*of**filiform**Lie**algebras**of**dimension*9, 10 and*11*. (In lower*dimensions*this is well known.) ... This paper is part*of*the PhD. thesis*of*the second author. She thanks CONICET for the Ph.D. fellowship awarded that made this possible. ...
« Previous

*Showing results 1 — 15 out of 389 results*