Related papers: A chain coalgebra model for the James map

An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are…

Trace map on deformation quantized algebra leads to the algebraic index theorem. In this paper, we investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and…

In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the…

We prove directly that if E is a directed graph in which every cycle has an entrance, then there exists a C*-algebra which is co-universal for Toeplitz-Cuntz-Krieger E-families. In particular, our proof does not invoke ideal-structure…

Given a graph $\Gamma$, one may conside the set $X$ of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of $\Gamma$ and their $K$-theory counterparts -- the $K$-theory of…

Let g be a differential graded Lie algebra and suppose given a contraction of chain complexes of g onto a general chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the…

We consider cohomology of diagrams of algebras by Beck's approach, using comonads. We then apply this theory to computing the cohomology of $\Psi$-rings. Our main result is that there is a spectral sequence connecting the cohomology of the…

Two independent sets of a graph are adjacent if they differ on exactly one vertex (i.e. we can transform one into the other by adding or deleting a vertex). Let $k$ be an integer. We consider the reconfiguration graph $TAR_k(G)$ on the set…

A {\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$ and a set $C=\bigsqcup_{v\in E^0}C_v$, where each $C_v$ is a partition of the set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$, such that…

The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…

We introduce a family of $C^*$-correspondences $X_\alpha$ naturally associated to every ordinal graph $\Lambda$. When $\Lambda$ is a directed graph, $X_0$ is isomorphic to the usual $C^*$-correspondence associated to a graph. We show that…

Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…

Cubical cochains are equipped with an associative product, dual to the Serre diagonal, lifting the graded commutative structure in cohomology. In this work we introduce through explicit combinatorial methods an extension of this product to…

We consider $K$-semialgebras for a commutative semiring $K$ that are at the same time $\Sigma$-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over…

We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of…

We prove that the graph C*-algebra $C^*(E)$ of a trimmable graph $E$ is $U(1)$-equivariantly isomorphic to a pullback C*-algebra of a subgraph C*-algebra $C^*(E'')$ and the C*-algebra of functions on a circle tensored with another subgraph…

In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as $K$-algebras. As a consequence, we…

We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…

This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful gauge invariant traces, where the gauge action of $\T^k$ is the canonical one. We give a sufficient condition for the existence of such a…

We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…