CS : Companion archive on complex structures



This archive is a companion to the paper
"Complex structures on indecomposable 6-dimensional nilpotent real Lie algebras".
It contains

The whole content of this archive can be downloaded by clicking to the following file:


CS.zip file

CONTENTS OF THE ARCHIVE :

o "readme.text"
o directory 6nilp with all commutation relations files for the algebras :
"6nilp/6nilp.1" (algebra g_{6.1})     "6nilp/6nilp.3" (algebra g_{6.3})     "6nilp/6nilp.4" (algebra g_{6.4})    
"6nilp/6nilp.5" (algebra g_{6.5})     "6nilp/6nilp.6" (algebra g_{6.6})     "6nilp/6nilp.7" (algebra g_{6.7})    
"6nilp/6nilp.8" (algebra g_{6.8})     "6nilp/m.5" (algebra M5)     "6nilp/m.10" (algebra M10)    
"6nilp/m.14-1" (algebra M14_{-1})     "6nilp/m.14+1" (algebra M14_{+1})     "6nilp/m.18-1" (algebra M18_{-1})    
"6nilp/m.18+1" (algebra M18_{+1})
o "program3_1.red"
"program3_1.red" computes the complex structures on the algebra g_{6,3} in the case xi(1,6) neq 0.
o "matJ3_1.red"
"matJ3_1.red" Reduce file containing the matrice J computed by this program.
o "rprogram3_1.tex"
"rprogram3_1.tex" result file (output) of the foregoing program
o "program3_2.red"
"program3_2.red" computes the complex structures on the algebra g_{6,3} in the case xi(1,6) = 0, xi(2,5) neq 0.
o "matJ3_2.red"
"matJ3_2.red" Reduce file containing the matrice J computed by this program.
o "rprogram3_2.tex"
"rprogram3_2.tex" result file (output) of the foregoing program
o "program3_3.red"
"program3_3.red" computes the complex structures on the algebra g_{6,3} in the case xi(1,6) = 0, xi(2,5) = 0.
o "matJ3_3.red"
"matJ3_3.red" Reduce file containing the matrice J computed by this program.
o "rprogram3_3.tex"
"rprogram3_3.tex" result file (output) of the foregoing program
o "program4.red"
"program4.red" computes the complex structures on the algebra g_{6,7}.
o "matJ4.red"
"matJ4.red" Reduce file containing the matrice J computed by this program.
o "rprogram4.tex"
"rprogram4.tex" result file (output) of the foregoing program
o "program5.red"
"program5.red" computes the complex structures on the algebra g_{6,4}.
o "matJ5.red"
"matJ5.red" Reduce file containing the matrice J computed by this program.
o "rprogram5.red"
"rprogram5.tex" result file (output) of the foregoing program
o "program6_1.red"
"program6_1.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,1) neq 0, xi(2,3) neq 0, xi(1,3) neq xi(2,4).
o "matJ6_1.red"
"matJ6_1.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_1.tex"
"rprogram6_1.tex" result file (output) of the foregoing program
o "program6_2.red"
"program6_2.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,1) neq 0, xi(2,3) = 0, xi(1,3) neq xi(2,4).
o "matJ6_2.red"
"matJ6_2.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_2.tex"
"rprogram6_2.tex" result file (output) of the foregoing program
o "program6_3.red"
"program6_3.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,1) neq 0, xi(1,3) = xi(2,4).
o "matJ6_3.red"
"matJ6_3.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_3.tex"
"rprogram6_3.tex" result file (output) of the foregoing program
o "program6_4.red"
"program6_4.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,1) = 0, xi(2,3) neq 0.
o "matJ6_4.red"
"matJ6_4.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_4.tex"
"rprogram6_4.tex" result file (output) of the foregoing program
o "program6_5.red"
"program6_5.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,1) = 0, xi(2,3) = 0.
o "matJ6_5.red"
"matJ6_5.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_5.tex"
"rprogram6_5.tex" result file (output) of the foregoing program
o "program6_6.red"
"program6_6.red" computes the complex structures on the algebra g_{6,1} in the case xi(2,3) neq 0.
o "matJ6_6.red"
"matJ6_6.red" Reduce file containing the matrice J computed by this program.
o "rprogram6_6.tex"
"rprogram6_6.tex" result file (output) of the foregoing program
o "program7.red"
"program7.red" computes the complex structures on the algebra g_{6,6}
o "matJ7.red"
"matJ7.red" Reduce file containing the matrice J computed by this program.
o "rprogram7.tex"
"rprogram7.tex" result file (output) of the foregoing program
o "program8.red"
"program8.red" computes the complex structures on the algebra g_{6,5}
o "matJ8.red"
"matJ8.red" Reduce file containing the matrice J computed by this program.
o "rprogram8.tex"
"rprogram8.tex" result file (output) of the foregoing program
o "program9.red"
"program9.red" computes the complex structures on the algebra g_{6,8}
o "matJ9.red"
"matJ9.red" Reduce file containing the matrice J computed by this program.
o "rprogram9.tex"
"rprogram9.tex" result file (output) of the foregoing program
o "program10_1.red"
"program10_1.red" computes the complex structures on the algebra M10 in the case xi(4,3) neq xi(2,1).
o "matJ10_1.red"
"matJ10_1.red" Reduce file containing the matrice J computed by this program.
o "rprogram10_1.tex"
"rprogram10_1.tex" result file (output) of the foregoing program
o "program10_2and3.red"
"program10_2and3.red" computes the complex structures on the algebra M10 in the case xi(4,3) = xi(2,1) and in each of the subcases
case 2.1 : xi(3,3) = xi(1,1)
case 2.2 : xi(3,3) neq xi(1,1).
o "matJ10_2.red"
"matJ10_2.red" Reduce file containing the matrice J computed by this program. in the case 2.1 : xi(3,3) = xi(1,1)
o "matJ10_3.red"
"matJ10_3.red" Reduce file containing the matrice J computed by this program. in the case 2.2 : xi(3,3) neq xi(1,1)
o "rprogram10_2and3.tex"
"rprogram10_2and3.tex" result file (output) of the foregoing program
o "program11_-1.red"
"program11_-1.red" proves there is no complex structures on the algebra M14_{-1}
o "rprogram11_-1.tex"
"rprogram11_-1.tex" result file (output) of the foregoing program
o "program11.red"
"program11.red" computes the complex structures on the algebra M14_{1}
o "matJ11.red"
"matJ11.red" Reduce file containing the matrice J computed by this program.
o "rprogram11.tex"
"rprogram11.tex" result file (output) of the foregoing program
o "program12_-1.red"
"program12_-1.red" proves there is no complex structures on the algebra M18_{-1}
o "rprogram12_-1.tex"
"rprogram12_-1.tex" result file (output) of the foregoing program
o "program12.red"
"program12.red" computes the complex structures on the algebra M18_{+1}
o "matJ12.red"
matJ12.red Reduce file containing the matrice J computed by this program.
o "rprogram12.tex"
"rprogram12.tex" result file (output) of the foregoing program
o "program13_1a.red"
"program13_1a.red" computes the complex structures on the algebra M5 in the case xi(2,4) neq 0.
o "matJ13_1a.red"
"matJ13_1a.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_1a.tex"
"rprogram13_1a.tex" result file (output) of the foregoing program
o "program13_1b.red"
"program13_1b.red" computes the complex structures on the algebra M5 in the case xi(2,3) neq 0.
o "matJ13_1b.red"
"matJ13_1b.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_1b.tex"
"rprogram13_1b.tex" result file (output) of the foregoing program
o "program13_21.red"
"program13_21.red" (subsubsection 13.2.1 of the paper) computes the complex structures on the algebra M5 in the case xi(2,1)*xi(2,4) neq 0.
o "matJ13_21.red"
"matJ13_21.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_21.tex"
"rprogram13_21.tex" result file (output) of the foregoing program
o "program13_22.red"
"program13_22.red" (subsubsection 13.2.2 of the paper) computes the complex structures on the algebra M5 in the case xi(2,1)*xi(2,3) neq 0, xi(2,4)=0.
o "matJ13_22.red"
"matJ13_22.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_22.tex"
"rprogram13_22.tex" result file (output) of the foregoing program
o "program13_23.red"
"program13_23.red" (subsubsection 13.2.3 of the paper) computes the complex structures on the algebra M5 in the case
xi(2,1) neq 0, xi(2,2)=xi(2,4)=0, xi(2,2) + xi(3,3) neq 0.
o "matJ13_23.red"
"matJ13_23.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_23.tex"
"rprogram13_23.tex" result file (output) of the foregoing program
o "program13_24.red"
"program13_24.red" (subsubsection 13.2.4 of the paper) computes the complex structures on the algebra M5 in the case
xi(2,1) neq 0, xi(2,2) = xi(2,4) = 0, xi(3,3) = -xi(2,2), xi(3,4) = -xi(2,1).
o "matJ13_24.red"
"matJ13_24.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_24.tex"
"rprogram13_24.tex" result file (output) of the foregoing program
o "program13_25.red"
"program13_25.red" (subsubsection 13.2.5 of the paper) computes the complex structures on the algebra M5 in the case
xi(2,1) neq 0, xi(2,2) = xi(2,4) = 0, xi(3,3) = -xi(2,2), xi(3,4) neq -xi(2,1).
o "matJ13_25.red"
"matJ13_25.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_25.tex"
"rprogram13_25.tex" result file (output) of the foregoing program
o "program13_3.red"
"program13_3.red" computes a local chart for the differentiable manifold $\mathfrak{X}_{M5}$ in the neighborhood of the canonical complex structure $J_0$
o "matJ13_3.red"
"matJ13_3.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_3.tex"
"rprogram13_3.tex" result file (output) of the foregoing program
o "program13_43.red"
"program13_43.red" (subsubsection 13.4.3 of the paper) computes the complex structures on the algebra M5
up to equivalence in the case 1 where B and C are not both 0.
o "matJ13_43.red"
"matJ13_43.red" Reduce file containing the matrice J computed by this program.
o "rprogram13_43.tex"
"rprogram13_43.tex" result file (output) of the foregoing program
o "program13_45case2_1.red"
"program13_45case2_1.red" (subsubsection 13.4.5 of the paper) computes the complex structures on the algebra M5
up to equivalence in the case 2 where B = C = 0 and the subcase case2.1 where xi(5,5) = 0.
o "rprogram13_45case2_1.tex"
"rprogram13_45case2_1.tex" result file (output) of the foregoing program
o "program13_45case2_2.red"
"program13_45case2_2.red" (subsubsection 13.4.5 of the paper) computes the complex structures on the algebra M5
up to equivalence in the case 2 where B = C = 0 and the subcase case2.2 where xi(5,5) neq 0.
o "rprogram13_45case2_2.tex"
"rprogram13_45case2_2.tex" result file (output) of the foregoing program