Quantum homomorphisms

Graph Homomorphisms for Quantum Players

A homomorphism from a graph X to a graph Y is an adjacency preserving mapping f : V (X)→ V (Y ). We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y . This is a generalization of the well-studied graph coloring game. Via systematic study of quantum homomorphisms we prove new results for graph coloring. Mos...

On Homomorphisms from Ringel-hall Algebras to Quantum Cluster Algebras

In [1],the authors defined algebra homomorphisms from the dual RingelHall algebra of certain hereditary abelian categoryA to an appropriate q-polynomial algebra. In the case that A is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in [9]. Moreover, if the underlying graph of Q is bipartite and the matrix B associated t...

Lattice Homomorphisms Induced by Group Homomorphisms

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

POMDP Homomorphisms

The problem of finding hidden state in a POMDP and the problem of finding abstractions for MDPs are closely related. In this paper, we analyze the connection between existing Predictive State Representation methods [3] and homomorphic reductions of Markov Processes [5, 6]. We formally define a POMDP homomorphism, then extend PSR reduction methods to find POMDP homomorphisms when the original PO...

n-Homomorphisms