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pro vyhledávání: '"46L85"'
Autor:
Nikolaev, Igor V.
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all axioms of
Externí odkaz:
http://arxiv.org/abs/2412.09148
In this paper, we construct a recursive subhomogeneous decomposition for the Cuntz--Pimsner algebras obtained from breaking the orbit of a minimal Hilbert $C(X)$-bimodule at a subset $Y \subset X$ with non-empty interior. This generalizes the known r
Externí odkaz:
http://arxiv.org/abs/2410.07424
Autor:
D'Andrea, Francesco
In this paper, we study multiplicative structures on the K-theory of the core $A:=C^*(E)^{U(1)}$ of the C*-algebra $C^*(E)$ of a directed graph $E$. In the first part of the paper, we study embeddings $E\to E\times E$ that induce a *-homomorphism $A\
Externí odkaz:
http://arxiv.org/abs/2410.06242
Autor:
Chirvasitu, Alexandru
A classical branched cover is an open surjection of compact Hausdorff spaces with uniformly bounded finite fibers and analogously, a quantum branched cover is a unital $C^*$ embedding admitting a finite-index expectation. We show that whenever a comp
Externí odkaz:
http://arxiv.org/abs/2409.17807
Autor:
Willett, Rufus
A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and recently advan
Externí odkaz:
http://arxiv.org/abs/2408.13350
Autor:
Nikolaev, Igor V.
Let $k$ be a number field and $V(k)$ an $n$-dimensional projective variety over $k$. We use the $K$-theory of a $C^*$-algebra $A_V$ associated to $V(k)$ to define a height of points of $V(k)$. The corresponding counting function is calculated and we
Externí odkaz:
http://arxiv.org/abs/2408.12020
Autor:
Nikolaev, Igor V.
We use $K$-theory of the $C^*$-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V\to Spec ~\mathbf{Z}$. In particular, it is proved that the Picard group of $V$ is isomorphic to the $K_0$-group of a Cuntz-Pi
Externí odkaz:
http://arxiv.org/abs/2406.17063
We show that every C*-algebra that is (m,n)-pure in the sense of Winter is already pure, that is, its Cuntz semigroup is almost unperforated and almost divisible. More generally, we show that even weaker comparison and divisibility properties automat
Externí odkaz:
http://arxiv.org/abs/2406.11052
Autor:
Nikolaev, Igor V.
We recast the local factors of the Hasse-Weil zeta function at infinity in terms of the Cuntz-Pimsner algebras. The nature of such factors is an open problem studied by Deninger and Serre.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2404.12179
We study the local-triviality dimensions of actions on $C^*$-algebras, which are invariants developed for noncommutative Borsuk-Ulam theory. While finiteness of the local-triviality dimensions is known to guarantee freeness of an action, we show that
Externí odkaz:
http://arxiv.org/abs/2403.06767