# 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 $G$.