- #1
JustMeDK
- 14
- 0
Any given representation (some matrices of some algebra) will be reducible if there exists a singular, but nonzero matrix S that commutes with all elements of the representation; conversely, if no such S exists, then the representation is irreducible. This is Schur's Lemma.
My question is: Does there exists some similar criterion for deciding whether or not a given representation is decomposable, i.e., whether or not there exists some change of basis that brings the representation on (sub)block-diagonal form?
My question is: Does there exists some similar criterion for deciding whether or not a given representation is decomposable, i.e., whether or not there exists some change of basis that brings the representation on (sub)block-diagonal form?