ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 18, 46, 47 Nassopoulos, George F., University of Athens, Greece Coproducts and projective presentations of operator algebras. Let B denote the category of unital involutive Banach algebras and their non-expansive homomorphisms and A its full reflective subcategory of C^{∗}- algebras. Coproducts are constructed qua modified tensor products [N] by defining a consistent involution, the tensor greatest cross-norm and further applying, the directed-limit technique. Besides, the unitary group functor U : A → Grp provides a faithful right adjoint to the group C^{∗}-algebra functor C^{∗} : Grp → A, the function algebra e(Γ, ℂ) on the circle group Γ therefore constituting a projective generator. Among various properties every C^{∗}-algebra admits of a projective presentation as a quotient of a suitable copower of E(Γ.ℂ), and analogous results for W^{∗}-algebras are obtained, convenient for homological purposes. Reference: G. F. Nassopoulos, On the existence of coproducts in the category of noncommutative algebras, Linear @ Multilinear Algebra 2 (1974), 39 -