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Question: Optimal Lie Algebra?

Question:Optimal Lie Algebra?

mskalsi 290 Maple
algebra geometry
March 14 2016
0

Dear All

Is there anybody who is working on contruction of optimal Lie algebra using Maple packages like DifferentialGeometry and LieAlgebra, I tried to find commands for constructing algebra in these packages but could not find such commands. I am sure these are only package that might help me. Following is Lie algebra whose optimal system is required:

 

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with(PDEtools, SymmetryCommutator, InfinitesimalGenerator):
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S[1], S[2], S[3], S[4], S[5], S[6], S[7], S[8], S[9], S[10], S[11] := [_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 1], [_xi[x] = 0, _xi[y] = t, _xi[t] = 0, _eta[u] = 0, _eta[v] = x], [_xi[x] = 0, _xi[y] = y, _xi[t] = 2*t, _eta[u] = -2*u, _eta[v] = -v], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = t], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 1, _eta[v] = y], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 1, _eta[u] = 0, _eta[v] = 0], [_xi[x] = 1, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 0], [_xi[x] = t, _xi[y] = 0, _xi[t] = 0, _eta[u] = 1, _eta[v] = 0], [_xi[x] = y, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 2*x], [_xi[x] = x, _xi[y] = 0, _xi[t] = -t, _eta[u] = 2*u, _eta[v] = 2*v], [_xi[x] = 0, _xi[y] = 1, _xi[t] = 0, _eta[u] = 0, _eta[v] = 0]

[_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 1], [_xi[x] = 0, _xi[y] = t, _xi[t] = 0, _eta[u] = 0, _eta[v] = x], [_xi[x] = 0, _xi[y] = y, _xi[t] = 2*t, _eta[u] = -2*u, _eta[v] = -v], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = t], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 0, _eta[u] = 1, _eta[v] = y], [_xi[x] = 0, _xi[y] = 0, _xi[t] = 1, _eta[u] = 0, _eta[v] = 0], [_xi[x] = 1, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 0], [_xi[x] = t, _xi[y] = 0, _xi[t] = 0, _eta[u] = 1, _eta[v] = 0], [_xi[x] = y, _xi[y] = 0, _xi[t] = 0, _eta[u] = 0, _eta[v] = 2*x], [_xi[x] = x, _xi[y] = 0, _xi[t] = -t, _eta[u] = 2*u, _eta[v] = 2*v], [_xi[x] = 0, _xi[y] = 1, _xi[t] = 0, _eta[u] = 0, _eta[v] = 0]

 (1)
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G[1] := InfinitesimalGenerator(S[1], [u(x, y, t), v(x, y, t)]); 1; G[2] := InfinitesimalGenerator(S[2], [u(x, y, t), v(x, y, t)]); 1; G[3] := InfinitesimalGenerator(S[3], [u(x, y, t), v(x, y, t)]); 1; G[4] := InfinitesimalGenerator(S[4], [u(x, y, t), v(x, y, t)]); 1; G[5] := InfinitesimalGenerator(S[5], [u(x, y, t), v(x, y, t)]); 1; G[6] := InfinitesimalGenerator(S[6], [u(x, y, t), v(x, y, t)]); 1; G[7] := InfinitesimalGenerator(S[7], [u(x, y, t), v(x, y, t)]); 1; G[8] := InfinitesimalGenerator(S[8], [u(x, y, t), v(x, y, t)]); 1; G[9] := InfinitesimalGenerator(S[9], [u(x, y, t), v(x, y, t)]); 1; G[10] := InfinitesimalGenerator(S[10], [u(x, y, t), v(x, y, t)]); 1; G[11] := InfinitesimalGenerator(S[11], [u(x, y, t), v(x, y, t)])

proc (f) options operator, arrow; diff(f, v) end proc

  

proc (f) options operator, arrow; t*(diff(f, y))+x*(diff(f, v)) end proc

  

proc (f) options operator, arrow; y*(diff(f, y))+2*t*(diff(f, t))-2*u*(diff(f, u))-v*(diff(f, v)) end proc

  

proc (f) options operator, arrow; t*(diff(f, v)) end proc

  

proc (f) options operator, arrow; diff(f, u)+y*(diff(f, v)) end proc

  

proc (f) options operator, arrow; diff(f, t) end proc

  

proc (f) options operator, arrow; diff(f, x) end proc

  

proc (f) options operator, arrow; t*(diff(f, x))+diff(f, u) end proc

  

proc (f) options operator, arrow; y*(diff(f, x))+2*x*(diff(f, v)) end proc

  

proc (f) options operator, arrow; x*(diff(f, x))-t*(diff(f, t))+2*u*(diff(f, u))+2*v*(diff(f, v)) end proc

  

proc (f) options operator, arrow; diff(f, y) end proc

 (2)
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Download Lie_Algebra_Classification.mwLie_Algebra_Classification.mw

   
 

 

 
   
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 (2)
 

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Regards
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