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lavster
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Im having difficulty understanding this satement - can someone please explain it to me...
let M be the class of mobius transformations
M is isomorphic to GL2/Diag isomorphic to SL2/Id, where GL2 is the group of non-degenerate matrices of size 2 x 2 with complex entries, SL2 = A in GL2 : detA = 1, Diag is the group of non-zero diagonal 2 x 2 matrices and Id is the identity.
I know what a mobius transform is and that the matrix of its coefficients cannot be zero, i know that isomorphism = one to one correspondence... but i don't understand this statement at all - why are we exclusing the diagonal matrices... surely we should be excluding the matrices with det 0?
thanks
let M be the class of mobius transformations
M is isomorphic to GL2/Diag isomorphic to SL2/Id, where GL2 is the group of non-degenerate matrices of size 2 x 2 with complex entries, SL2 = A in GL2 : detA = 1, Diag is the group of non-zero diagonal 2 x 2 matrices and Id is the identity.
I know what a mobius transform is and that the matrix of its coefficients cannot be zero, i know that isomorphism = one to one correspondence... but i don't understand this statement at all - why are we exclusing the diagonal matrices... surely we should be excluding the matrices with det 0?
thanks