20,109 research outputs found
Nuclearity of semigroup C*-algebras and the connection to amenability
We study C*-algebras associated with subsemigroups of groups. For a large
class of such semigroups including positive cones in quasi-lattice ordered
groups and left Ore semigroups, we describe the corresponding semigroup
C*-algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full
corners in associated group crossed products. These descriptions allow us to
characterize nuclearity of semigroup C*-algebras in terms of faithfulness of
left regular representations and amenability of group actions. Moreover, we
also determine when boundary quotients of semigroup C*-algebras are UCT
Kirchberg algebras. This leads to a unified approach to Cuntz algebras and ring
C*-algebras.Comment: 42 pages; revised version, corrected typo
Constructing cell data for diagram algebras
We show how the treatment of cellularity in families of algebras arising from
diagram calculi, such as Jones' Temperley--Lieb wreaths, variants on Brauer's
centralizer algebras, and the contour algebras of Cox et al (of which many
algebras are special cases), may be unified using the theory of tabular
algebras. This improves an earlier result of the first author (whose hypotheses
covered only the Brauer algebra from among these families).Comment: Approximately 38 pages, AMSTeX. Revised in light of referee comments.
To appear in the Journal of Pure and Applied Algebr
Isometries on Banach algebras of vector-valued maps
We propose a unified approach to the study of isometries on algebras of
vector-valued Lipschitz maps and those of continuously differentiable maps by
means of the notion of admissible quadruples. We describe isometries on
function spaces of some admissible quadruples that take values in unital
commutative -algebras. As a consequence we confirm the statement of
\cite[Example 8]{jp} on Lipschitz algebras and show that isometries on such
algebras indeed take the canonical form.Comment: 35 page
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