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 Mn(Z) or Mn(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 Mn(Z) or Mn(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.
V2.28, 13 July 2023