On Homomorphisms of Matrix Algebras of Continuous Functions
نویسنده
چکیده
If X is a topological space we denote by C(X) ® Mn the algebra of continuous functions from X to the algebra Mn of n x n complex matrices. A complete characterization of those topological spaces Y is given (in terms of vector bundles on Y) such that each unital algebrahomomorphism Φ: C(X) Θ Mn —• C(Y) Mkn is of the form a o (Φ' ® idΛ) for some homomorphism Φ': C(X) -+ C(Y) ® Λ/* and some suitable inner (or C(Ύ)-linear) automorphism a of the algebra C ( 7 ) ® Λ/fc,. In particular this decomposition is assured provided that Y is a finite CW-complex of dimension < 2k and K°{Y) does not have /?-torsion.
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