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1. 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

2. 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