相关论文: Do phantom Cuntz-Krieger algebras exist?

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…

We consider a class of complete Kahler manifolds with a strictly pseudoconvex boundary at infinity. After studying its asymptotic geometry, we formulate a conjecture in the Kahler-Einstein case relating the bottom of spectrum to the CR…

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

We prove the Lefchetz theorem for CR submanifolds in Hermitian symmetric spaces. As an application we prove the nonexistence of real analytic Levi flat submanifolds in such manifolds.

We derive universal properties of the near-horizon geometry of spherically symmetric black holes that follow from the observability of a regular apparent horizon. Only two types of solutions are admissible. After reviewing their properties…

Let k a characteristic zero field. We give a characterization for the finite quiver k-algebras, based on double derivations. More precisely, we prove that if an associative and unitary k-algebra have a family of double derivations…

Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite…

There has been much discussion on the possibility of firewalls at the horizon-scale in black hole physics, including questions regarding the presence or absence of firewalls at apparent horizons, such as the Rindler horizon and the horizon…

We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.

We consider Borcherds algebras with no real roots and the property that all zeroes in the Borcherds Cartan matrix occur in a single diagonal zero block. It follows that all other entries of the matrix are negative. We give a structure…

Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gr\"obner basis implies the existence of a Koszul filtration for…

Let ${\cal Z}$ be the Jiang-Su algebra and ${\cal K}$ the C*-algebra of compact operators on an infinite dimensional separable Hilbert space. We prove that the corona algebra $M({\cal Z}\otimes {\cal K})/{\cal Z}\otimes {\cal K}$ has real…

It is well-known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing…

A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric…

We give several examples of tilting-discrete symmetric algebras; in particular, one explores which algebra has tilting-discrete trivial extension. We provide a counter example of the conjecture stating any {\tau} -tilting finite symmetric…

It is well known that real zeros of the Riemann zeta function are negative even integers. As for real zeros of the Hurwitz zeta function, T. Nakamura recently gave an existence condition in the intervals (0,1) and (-1,0). We generalize this…

In this paper, we give a characterization of tau-rigid-finite algebras with radical square zero in terms of the separated quivers, which is an analog of a famous characterization of representation-finite algebras with radical square zero.

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius…

We provide examples of ambient nuclear C*-algebras of non-nuclear C*-algebras with no proper intermediate C*-algebras. In particular this gives the first examples of minimal ambient nuclear C*-algebras of non-nuclear C*-algebras. For this…