Decomposable Leavitt path algebras for arbitrary graphs

Abstract

For any field K and for a completely arbitrary graph E, we characterize the Leavitt path algebras LK(E) that are indecomposable (as a direct sum of two-sided ideals) in terms of the underlying graph. When the algebra decomposes, it actually does so as a direct sum of Leavitt path algebras for some suitable graphs. Under certain finiteness conditions, a unique indecomposable decomposition exists. © by De Gruyter 2015.