Related papers: Tate curves and UHF-algebras

By the curve shortening flow, the only closed embedded contracting self-similar solutions are circles: we give a very short and intuitive geometric proof of this basic and classical result using an idea of Gage.

Let $T$ be a densely defined closed symmetric operator with equal deficiency indices in a separable complex Hilbert space $H$. In this paper, we prove that $T$ has a self-adjoint extension with compact resolvent if and only if the domain…

Tate-Hochschild cohomology of an algebra is a generalization of ordinary Hochschild cohomology, which is defined on positive and negative degrees and has a ring structure. Our purpose of this paper is to study the eventual periodicity of an…

We show that de Rham--Witt forms are naturally isomorphic to $p$-typical curves on $p$-adic Tate twists, which answers a question of Artin--Mazur from 1977 pursued in the earlier work of Bloch and Kato. We show this by more generally…

Perfectoid versions of Abel Jacobi and Reimann Roch Theorem are proved, and perfectoid Elliptic Curve is constructed. A Perfectoid Tate Curve is defined and its cohomology computed via a \v{C}ech complex. Furthermore, perfectoid Theta…

Quantum geometry of twisted Wess--Zumino--Witten branes is formulated in the framework of twisted Reflection Equation Algebras. It is demonstrated how the representation theory of these algebras leads to the correct classification and…

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…

We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…

We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding…

Let L be a p-adic local field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) is a stably flat completion of its universal enveloping algebra. As a consequence the relative cohomology for the…

The Tait-Kneser theorem states that the osculating circles of a plane curve with monotonic curvature are pairwise disjoint and nested. We discuss this theorem and a number of its variations.

We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.

To each finitely aligned higher-rank graph $\Lambda$ and each $\mathbb{T}$-valued 2-cocycle on $\Lambda$, we associate a family of twisted relative Cuntz-Krieger algebras. We show that each of these algebras carries a gauge action, and…

Let $\mathfrak{g}$ be a finite-dimensional real or complex Lie algebra, and let $\mu \in \mathfrak{g}^{*}$. In the first part of the paper, the relation is discussed between the derived algebra of the stabilizer of $\mu$ and the set of…

In this work we consider the Gutt star product viewed as an associative deformation of the symmetric algebra S^\bullet(g) over a Lie algebra g and discuss its continuity properties: we establish a locally convex topology on S^\bullet(g)…

Let $\mathbb{X}$ be a weighted projective line and $\operatorname{coh}\mathbb{X}$ the associated categoy of coherent sheaves. We classify the tilting complexes $T$ in $D^b(\operatorname{coh}\mathbb{X})$ such that $\tau^2 T\cong T$, where…

In this paper, for an arbitrary Kac-Moody Lie algebra $\mathfrak g$ and a diagram automorphism $\mu$ of $\mathfrak g$ satisfying certain natural linking conditions, we introduce and study a $\mu$-twisted quantum affinization algebra…

Glimm's theorem says that a UHF algebra is almost embedded in a separable $C^*$-algebra not of type I. Applying his methods we obtain a covariant version of his result; a UHF algebra with a product type automorphism is covariantly embedded…

We prove that solutions $u$ of the equation $f=u-u\circ T$ are automatically Holder continuous when $f$ is Holder continuous, and $T$ is non uniformly expanding and Markov. This result applies in particular to Young towers and to…

We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.