Operations for Matrix Lie Algebras

This section describes the functionality provided for matrix Lie algebras which is additional to that provided for structure constant Lie algebras. For further information see Chapter Matrix Algebras.

BaseModule(M): AlgMatLie -> ModTupRng

The natural module on which the matrix Lie algebra \(M\) acts.

Generic(M): AlgMatLie -> AlgMatLie

The full matrix algebra in which the matrix Lie algebra \(M\) is naturally embedded.

Kernel(X): AlgMatLieElt -> ModTupRng

Nullspace(X): AlgMatLieElt -> ModTupRng

The kernel of the homomorphism represented by the Lie matrix algebra element \(X\).

NullspaceOfTranspose(X): AlgMatLieElt -> ModTupRng

RowNullSpace(X): AlgMatLieElt -> ModTupRng

The row nullspace of the homomorphism represented by the Lie matrix algebra element \(X\).