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Edited question:

Are there any other non-trivial *-homomorphisms between matrix algebras apart from the unitary homomorphisms?

Original question:

Does there exist a surjective (but not bijective) *-homomorphism between matrix algebras over the complex numbers? If so, are there any nice examples?

Note:

(I am excluding the case when one of had not realized the matrix algebras is simply were simple but since they are, the 1x1 matrix algebra.answer to the original question is indeed obvious)

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# *-homomorphisms between matrix algebras

Does there exist a surjective (but not bijective) *-homomorphism between matrix algebras over the complex numbers? If so, are there any nice examples?

Note: I am excluding the case when one of the algebras is simply the 1x1 matrix algebra.