The transformation algebras of Bernstein graph algebras

In this chapter we present a decomposition of the subalgebra T(G) of Hom(A(G)) generated by {id(A(G))} boolean OR {L-t vertical bar L-t: A(G) -> A(G), t is an element of A(G)}, where G is a graph, A(G) is the Bernstein graph algebra of G, idA(l) is the identity function on A(G) and L-t is the left (= right) multiplication by t. If G is a simple connected graph, without loop and vertical bar V(G)vertical bar > 2, then we present a characterization of T(G).