1,076 research outputs found
The Mathematics of Ivo Rosenberg
International audienceThis paper is dedicated to the memory of the distinguished scholar and friend Professor I.G .Rosenberg. We survey some of his most well known and not so known results, as well as present some new ones related to the study of maximal partial clones and their intersections
Localizing subcategories in the Bootstrap category of separable C*-algebras
Using the classical universal coefficient theorem of Rosenberg-Schochet, we
prove a simple classification of all localizing subcategories of the Bootstrap
category of separable complex C*-algebras. Namely, they are in bijective
correspondence with subsets of the Zariski spectrum of the integers --
precisely as for the localizing subcategories of the derived category of
complexes of abelian groups. We provide corollaries of this fact and put it in
context with similar classifications available in the literature.Comment: 9 pages, simplified proof. Final version, to appear on J. of K-theor
Gorenstein homological algebra and universal coefficient theorems
We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories
Gorenstein homological algebra and universal coefficient theorems
We study criteria for a ring - or more generally, for a small category - to
be Gorenstein and for a module over it to be of finite projective dimension.
The goal is to unify the universal coefficient theorems found in the literature
and to develop a machinery for proving new ones.
Among the universal coefficient theorems covered by our methods we find,
besides all the classic examples, several exotic examples arising from the
KK-theory of C*-algebras and also Neeman's Brown-Adams representability theorem
for compactly generated categories.Comment: 43 page
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