Endomorphisms

EndomorphismRing(G): GrpMat -> AlgMat

EndomorphismAlgebra(G): GrpMat -> AlgMat

For an integral or rational matrix group \(G\), return the endomorphism ring (i.e. the commuting algebra) of \(G\) as a subalgebra of \(M_n({\mathbb{Z}})\) or \(M_n({\mathbb{Q}})\) respectively.

CentreOfEndomorphismRing(G): GrpMat -> AlgMat

CentreOfEndomorphismAlgebra(G): GrpMat -> AlgMat

For an integral or rational matrix group \(G\), return the center of the endomorphism ring (i.e. the commuting algebra) of \(G\) as a subalgebra of \(M_n({\mathbb{Z}})\) or \(M_n({\mathbb{Q}})\) respectively.

DimensionOfEndomorphismRing(G): GrpMat -> RngIntElt

Return the dimension of the endomorphism ring of an integral or rational matrix group \(G\) by a modular method.

DimensionOfCentreOfEndomorphismRing(G): GrpMat -> RngIntElt

Return the dimension of the centre of the endomorphism ring of an integral or rational matrix group \(G\) by a modular method.

Endomorphisms(G, n): GrpMat, RngIntElt -> [ AlgMatElt ]

For an integral or rational matrix group \(G\), return a sequence containing \(n\) independent endomorphisms of \(G\). \(n\) must be in the range \([0 .. d]\), where \(d\) is the dimension of the endomorphism ring of \(G\).

CentralEndomorphisms(G, n): GrpMat, RngIntElt -> [ AlgMatElt ]

For an integral or rational matrix group \(G\), return a sequence containing \(n\) independent central endomorphisms of \(G\). \(n\) must be in the range \([0 .. d]\), where \(d\) is the dimension of the centre of the endomorphism ring of \(G\).