Explicit construction of universal operator algebras and applications to polynomial factorization

Abstract

Using the characterization of unital operator algebras developed in [6], we give explicit internal definitions of the free product and the maximal operator-algebra tensor product of operator algebras and of the group operator algebra OA ( G ) {\text {OA}}(G) of a discrete semigroup G G (if G G is a discrete group, then OA ( G ) {\text {OA}}(G) coincides with the group C ∗ {C^ * } -algebra C ∗ ( G ) ) {C^*}(G)) ). This approach leads to new factorization theorems for polynomials in one and two variables.