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Willie Cortiñas
เข้าร่วมเมื่อ 6 ก.ย. 2020
GeNoCAS 2024: Pere Ara
Title: The Cuntz semigroup of a ring
Abstract: For any ring R we introduce an invariant in the form of a partially ordered abelian semigroup S(R) built from an equivalence relation on the class of countably generated projective modules. We call S(R) the Cuntz semigroup of the ring R. This construction is akin to the manufacture of the Cuntz semigroup of a C*-algebra using countably generated Hilbert modules. We provide computations for S(R) for unit-regular rings and for semilocal rings, and relate our construction to the Cuntz semigroup of a C*-algebra.
We will also describe the ideals of the ring R which are detected by the semigroup S(R), and we will show that the restriction of S(-) to a large class of rings, called left normal rings, provides a continuous functor from the corresponding full subcategory of rings to the category Cu of abstract Cuntz semigroups.
This is joint work with Ramon Antoine (UAB), Joan Bosa (Zaragoza), Francesc Perera (UAB) and Eduard Vilalta (Chalmers University).
Abstract: For any ring R we introduce an invariant in the form of a partially ordered abelian semigroup S(R) built from an equivalence relation on the class of countably generated projective modules. We call S(R) the Cuntz semigroup of the ring R. This construction is akin to the manufacture of the Cuntz semigroup of a C*-algebra using countably generated Hilbert modules. We provide computations for S(R) for unit-regular rings and for semilocal rings, and relate our construction to the Cuntz semigroup of a C*-algebra.
We will also describe the ideals of the ring R which are detected by the semigroup S(R), and we will show that the restriction of S(-) to a large class of rings, called left normal rings, provides a continuous functor from the corresponding full subcategory of rings to the category Cu of abstract Cuntz semigroups.
This is joint work with Ramon Antoine (UAB), Joan Bosa (Zaragoza), Francesc Perera (UAB) and Eduard Vilalta (Chalmers University).
มุมมอง: 30
วีดีโอ
GeNoCAS 2024: Scott Schmieding
มุมมอง 31หลายเดือนก่อน
Symbolic dynamics, strong shift equivalence, and the stable algebra of matrices. I'll discuss some connections between symbolic dynamical systems and K-theory, primarily through the shift and strong shift equivalence relations on matrices, introduced by Williams in 'the early 70's' as a tool for studying the classification problem for shifts of finite type. I'll give some background on this pro...
GeNoCAS 2024: Rufus Willett
มุมมอง 35หลายเดือนก่อน
Conditional representation stability and K-theory Roughly, a group G is stable if any approximate representation (i.e. a map into a unitary group that comes close to satisfying the representations defining the group) is itself close to an honest representation. If 'close' is interpreted in terms of the operator norm, this is known to be obstructed by K-theoretic invariants: this goes back to wo...
GeNoCAS 2024: Roberto Hernández Palomares
มุมมอง 39หลายเดือนก่อน
Quantum graphs, subfactors and tensor categories Graphs and their noncommutative analogues are interesting objects of study from the perspectives of operator algebras, quantum information and category theory. In this talk we will introduce equivariant graphs with respect to a quantum symmetry along with examples such as classical graphs, Cayley graphs of finite groupoids, and their quantum anal...
GeNoCAS 2024: Efren Ruiz
มุมมอง 342 หลายเดือนก่อน
The Algebraic Kirchberg-Phillips Question for Leavitt Path Algebras An open question in the theory of Leavitt path algebras is whether the pointed K-theory is a complete isomorphism invariant for unital, simple, purely infinite Leavitt path algebras over finite graphs. An important test case is to determine whether L_2 and L_{2^-} are isomorphic, where L_2 is the Leavitt path algebra of the gra...
GeNoCAS 2024: Christopher Schafhauser
มุมมอง 432 หลายเดือนก่อน
KK-rigidity of simple nuclear C*-algebras A landmark result in C*-algebra theory is the classification of unital separable simple nuclear Z-stable C*-algebras satisfying the universal coefficient theorem (UCT) in terms of their K-theory and traces. I will discuss this result with a focus on the role of UCT and the question of whether this assumption is necessary.
Moves for Bergman algebras
มุมมอง 412 หลายเดือนก่อน
In this talk we define Bergman presentations and Bergman algebras associated to Bergman presentations. These algebras embrace various generalisations of Leavitt path algebras. A Bergman presentation can be visualised by a Bergman graph, which is a finite bicoloured hypergraph satisfying two conditions. We define several moves for Bergman graphs and show that they preserve the isomorphism class ...
GeNoCAS 2024: Thaísa Tamusiunas
มุมมอง 283 หลายเดือนก่อน
Galois theory under inverse semigroup actions In this talk, we discuss the relationship between inverse semigroups and groupoids, as well as how E-unitary inverse semigroup actions relate to partial group actions. We also explore how these concepts contribute to the development of a Galois theory for inverse semigroup actions on rings.
GeNoCAS 2024: Devarshi Mukherjee
มุมมอง 465 หลายเดือนก่อน
Analytic K-theory for bornological spaces Abstract: We describe a version of algebraic K-theory for bornological algebras, using Efimov's recently developed continuous K-theory. When restricted to suitable analytic spaces over non-archimedean fields, our invariant satisfies Nisnevich descent, extending Thomason-Trobaugh's result for schemes. Joint with Jack Kelly and Federico Bambozzi.
GeNoCAS 2024: Federico Bambozzi
มุมมอง 1015 หลายเดือนก่อน
Non-commutative derived geometry I will sketch the definition of a topology on the category of differential graded algebras that is analogous to the classical Zariski topology. I will first recall the problems that arise when more direct approaches are attempted and emphasize how the derived setting permits overcoming such difficulties. Relations with previous works and some explicit computatio...
GeNoCAS 2024: Arun Soor
มุมมอง 946 หลายเดือนก่อน
Six-functor formalism for quasi-coherent analytic D-modules on rigid varieties I will try to explain a relatively simple way to obtain a six-functor formalism (in the sense of Lucas Mann) for analytic D-modules on rigid varieties, using a recently developed theory of quasi-coherent sheaves on rigid-analytic varieties (based on bornological spaces). This work is similar in spirit to work of Rodr...
GeNoCAS 2024: Ulrich Pennig
มุมมอง 716 หลายเดือนก่อน
Topological Invariants for G-kernels and Group Actions A G-kernel is a group homomorphism from a (discrete) group G to Out(A), the outer automorphism group of a C*-algebra A. There are cohomological obstructions to lifting such a G-kernel to a group action. In the setting of von Neumann algebras, G-kernels on the hyperfinite II_1-factor have been completely understood via deep results of Connes...
GeNoCAS 2024: Jamie Gabe
มุมมอง 376 หลายเดือนก่อน
Generalized homomorphisms and KK with extra structure In the 1980's, Cuntz developed a new approach to KK-theory by considering *-homomorphisms out of a certain universal algebra qA. For purposes of (in particular) classification of nuclear C*-algebras, one often considers different variations of KK-theory, such as Skandalis' nuclear KK-theory, Kirchberg's ideal-related KK-theory, or equivarian...
GeNoCAS 2024: Ben Steinberg
มุมมอง 386 หลายเดือนก่อน
Simplicity of Nekrashevych algebras of contracting self-similar groups Nekrashevych introduced C*-algebras and rings associated to self-similar groups. These algebras are ample groupoid algebras where the groupoids are minimal and effective, but rarely Hausdorff. It is therefore natural to consider simplicity for these algebras. In this talk I will discuss joint work with N. Szakacs (Manchester...
GeNoCAS 2024: Alistair Miller
มุมมอง 596 หลายเดือนก่อน
Correspondences, homology and $K$-theory for étale groupoids One approach to understanding the K-theory of an étale groupoid C*-algebra is to approximate it with the groupoid homology. I'll describe the functoriality of the K-theory, the homology and the approximation with respect to a class of groupoid morphisms called étale correspondences. These are a broad class of morphisms encompassing bo...
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