displays the commutator table and gives the stucture constants for the Lie algebra L.
CommutatorTable[L, V]
displays the commutator table and gives the stucture constants for the subalgebra V of the Lie algebra L.
CommutatorTable[L, rules]
displays the commutator table for Lie algebra L using the indexes provided by the set rules.
  • The Lie algebra L can be provided either from its structure constants or their infinitesimal generator representation.
  • The Lie subalgebra V is expressed by a span of base elements represented using the symbol X.
  • The optional argument rules consist of a list rules that denote each element on what element of the original Lie algebra correspond. If ommitted, the base elemets will be re-indexed accordingly.
  • The following options can be given :
ShowTableTruewhether to print the commutator table
ShowInfoFalsewhether to print any information about the Lie algebra
Click for copyable input
Let the Lie algebra
Click for copyable input
the commutator table and its structure constants are:
The commutator table and structure constants for a subalgebra are:
You can retrieve the commutator table from the structure constants by giving the command:
note that by ommiting the second argument the base elements that span this subalagbera were reindexed. To obtain the commutator table with respect to the original Lie algebra one has to give:
When a subset is chosen that is not a subalgebra a message will be printed: