Centers of path algebras, Cohn and Leavitt path algebras
  We study the center of several types of path algebras. We start with the path algebra $KE$ and prove that if the number of vertices is infinite then the center is zero. Otherwise, it coincides with the field $K$ except when the graph $E$ is a cycle in which case the center is $K[x]$, the polynomial algebra in one indeterminate. Then we compute the centers of prime Cohn and Leavitt path algebras. A lower and an upper bound for the center of a Leavitt path algebra are given by introducing the graded Baer radical for graded algebras. 
Mar\'ia Guadalupe Corrales Garc\'ia, Dolores Mart\'in Barquero,   C\'andido Mart\'in Gonz\'alez, Mercedes Siles Molina and J...
math.RA