Related papers: You Can See the Arrows in a Quiver Operator Algebr…

This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…

We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the…

We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the…

Let $\A$ and $\B$ be operator algebras with $c_0$-isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically isomorphic, then $\A$ and $\B$ are isometrically isomorphic.…

We show that if two tensor algebras of topological graphs are algebraically isomorphic, then the graphs are locally conjugate. Conversely, if the base space is at most one dimensional and the edge space is compact, then locally conjugate…

We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Delta-equivalent, if and only if they have completely isometric normal representations a, b on Hilbert spaces H, K respectively and there…

To determine that two given undirected graphs are isomorphic, we construct for them auxiliary graphs, using the breadth-first search. This makes capability to position vertices in each digraph with respect to each other. If the given graphs…

We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.

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…

An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…

Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected…

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.

We prove that if two path algebras with homogeneous relations are isomorphic as algebras, then they are isomorphic as graded path algebras. This extends a result by Bell and Zhang in the connected case.

Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably…

Two emerging topics in graph theory are the study of cospectral vertices of a graph, and the study of isospectral reductions of graphs. In this paper, we prove a fundamental relationship between these two areas, which is that two vertices…

A graph is said to be circular-arc if the vertices can be associated with arcs of a circle so that two vertices are adjacent if and only if the corresponding arcs overlap. It is proved that the isomorphism of circular-arc graphs can be…

Suppose we are given two graphs on $n$ vertices. We define an observable in the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with certainty if the graphs are isomorphic and ``no'' with probability at least…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. 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…

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…