Macaulay2 » Documentation
Packages » ExteriorExtensions » ExteriorExtension » LieAlg2Matrix
next | previous | forward | backward | up | index | toc

LieAlg2Matrix -- Converts from the LieAlgebra to Matrix form (with the standard basis)

Description

Let's build a 7-graded algebra and see the bases of each piece and see the elements of the (symbolic) Lie algebra get converted to matrices

i1 : ea = exteriorExtension(3, 7, QQ);
 
i2 : sln = ea.LieAlgebra;
 
i3 : (gens sln)#0

o3 = h
      1

o3 : sln
 
i4 : ea.LieAlg2Matrix (gens ea.LieAlgebra)#0

o4 = | 1 0  0 0 0 0 0 |
     | 0 -1 0 0 0 0 0 |
     | 0 0  0 0 0 0 0 |
     | 0 0  0 0 0 0 0 |
     | 0 0  0 0 0 0 0 |
     | 0 0  0 0 0 0 0 |
     | 0 0  0 0 0 0 0 |

               7        7
o4 : Matrix sln  <-- sln

For the programmer

The object LieAlg2Matrix is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ExteriorExtensions.m2:816:0.