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1. CJM 2016 (vol 68 pp. 1067)

Runde, Volker; Viselter, Ami
 On Positive Definiteness over Locally Compact Quantum Groups The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups. Keywords:bicrossed product, locally compact quantum group, non-commutative $L^p$-space, positive-definite function, positive-definite measure, separation propertyCategories:20G42, 22D25, 43A35, 46L51, 46L52, 46L89

2. CJM 2011 (vol 63 pp. 798)

Daws, Matthew
 Representing Multipliers of the Fourier Algebra on Non-Commutative $L^p$ Spaces We show that the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative $L^p$ spaces associated with the right von Neumann algebra of $G$. The resulting image is the idealiser of the image of the Fourier algebra. If these spaces are given their canonical operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative $L^p$ spaces we construct and show that they are completely isometric to those considered recently by Forrest, Lee, and Samei. We improve a result of theirs about module homomorphisms. We suggest a definition of a Figa-Talamanca-Herz algebra built out of these non-commutative $L^p$ spaces, say $A_p(\widehat G)$. It is shown that $A_2(\widehat G)$ is isometric to $L^1(G)$, generalising the abelian situation. Keywords:multiplier, Fourier algebra, non-commutative $L^p$ space, complex interpolationCategories:43A22, 43A30, 46L51, 22D25, 42B15, 46L07, 46L52

3. CJM 2008 (vol 60 pp. 379)

rgensen, Peter J\o
 Finite Cohen--Macaulay Type and Smooth Non-Commutative Schemes A commutative local Cohen--Macaulay ring $R$ of finite Cohen--Macaulay type is known to be an isolated singularity; that is, $\Spec(R) \setminus \{ \mathfrak {m} \}$ is smooth. This paper proves a non-commutative analogue. Namely, if $A$ is a (non-commutative) graded Artin--Schelter \CM\ algebra which is fully bounded Noetherian and has finite Cohen--Macaulay type, then the non-commutative projective scheme determined by $A$ is smooth. Keywords:Artin--Schelter Cohen--Macaulay algebra, Artin--Schelter Gorenstein algebra, Auslander's theorem on finite Cohen--Macaulay type, Cohen--Macaulay ring, fully bounded Noetherian algebra, isolated singularity, maximal Cohen--Macaulay module, non-commutative Categories:14A22, 16E65, 16W50
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