Related papers: Projections in Graph W*-Algebras
It is shown that the algebra of continuous functions on the quantum $2n+1$-dimensional lens space $C(L^{2n+1}_q(N; m_0,\ldots, m_n))$ is a graph $C^*$-algebra, for arbitrary positive weights $ m_0,\ldots, m_n$. The form of the corresponding…
We describe two kinds of regular invariant measures on the boundary path space of a second countable topological graph, which allows us to describe all extremal tracial weights on the graph C$^{*}$-algebra which are not gauge-invariant.…
Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
To a directed graph $E$ is associated a $C^*$-algebra $C^* (E)$ called a graph $C^*$-algebra. There is a canonical action $\gamma$ of ${\bf T}$ on $C^* (E)$, called the gauge action. In this paper we present necessary and sufficient…
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial classification of Hom-algebras over a PROP…
We characterise gaps in the full homomorphism order of graphs.
We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
Let $M$ be a K\"ahler manifold with complex structure $J$ and K\"ahler metric $g$. A c-projective vector field is a vector field on $M$ whose flow sends $J$-planar curves to $J$-planar curves, where $J$-planar curves are analogs of what…
Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal…
The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional and projectivity. Examples and closure properties are…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We introduce quiver gauge theory associated with the non-simply-laced type fractional quiver, and define fractional quiver W-algebras by using construction of arXiv:1512.08533 and arXiv:1608.04651 with representation of fractional quivers.
On overview of Coxeter groups $W$, their Iwahori-Hecke algebras $H$, Lusztig's asymptotic algebras $J$, cellular algebras in general and cellularity of $H$ in particular, as well as an introduction to Gyoja's $W$-graph algebra and the…
We characterise when the Leavitt path algebras over $\mathbb{Z}$ of two arbitrary countable directed graphs are $*$-isomorphic by showing that two Leavitt path algebras over $\mathbb{Z}$ are $*$-isomorphic if and only if the corresponding…
In this survey, we discuss the description of Vaksman-Soibelman quantum spheres using graph C*-algebras, following the seminal work of Hong and Szyma\'nski. We give a slightly different proof of the isomorphism with a graph C*-algebra,…
In recent years, with the rapid enhancement of computing power, deep learning methods have been widely applied in wireless networks and achieved impressive performance. To effectively exploit the information of graph-structured data as well…