Macaulay2 » Documentation
Packages » LieTypes :: embedding
next | previous | forward | backward | up | index | toc

embedding -- gives the embedding of Cartan subalgebras of one Lie algebra into another

Description

i1 : h=simpleLieAlgebra("F",4)

o1 = h

o1 : simple LieAlgebra
i2 : g=subLieAlgebra(h,{0,1}); describe g

o3 = 𝔞
      2
i4 : embedding(g,h)

o4 = | -2 1 |
     | -3 0 |
     | -2 0 |
     | -1 0 |

              4       2
o4 : Matrix ZZ  <-- ZZ
i5 : embedding(subLieAlgebra(h,"principal"),h)

o5 = | 22 |
     | 42 |
     | 30 |
     | 16 |

              4       1
o5 : Matrix ZZ  <-- ZZ

Ways to use embedding:

  • embedding(LieAlgebra,LieAlgebra)

For the programmer

The object embedding is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/LieTypes.m2:1648:0.