A Functorial Approach to Group C∗-Algebras
نویسندگان
چکیده
Let A be the category of unital C∗-algebras. A counterexample is given to show that the unitary group functor U : A −→ Grp (and hence the composite of the forgetful functor G : Grp −→ Set with U) although being a faithful right adjoint, fails to be algebraic even in the commutative case. In so doing, a canonical presentation of any unital C∗-algebra as a quotient of a free product of copies (i.e., a copower in A) of C(S1, C) is obtained, leading to an alternative characterization of compact Hausdorff spaces, as well. Isomorphism questions are also considered. Mathematics Subject Classification (2000): Primary 22D25, 54D30; Secondary 18A40, 43A95, 46L05
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تاریخ انتشار 2008