Wreath products by a Leavitt path algebra and affinizations. (Q2923342)

Starting from an associative algebra \(A\) and a graph \(\Gamma=(V,E)\), the authors construct the wreath product \(B:=A\text{\,wr\,}L(\Gamma)\) of \(A\) and the Leavitt path algebra \(L(\Gamma)\). The algebra \(B\) has an ideal \(I\) consisting of (possibly infinite) matrices over \(A\) and such that \(B/I\cong L(\Gamma)\). Moreover if \(W\) is a hereditary subset of the set of vertices of a graph \(\Gamma\), then the Leavitt path algebra \(L(\Gamma)\) can be written as a wreath product of \(L(W)\) with \(L(\Gamma/W)\) (for a suitable notion of quotient graph). The authors take advantage of these facts to construct new examples of (i) affine algebras with non-nil Jacobson radicals, (ii) affine algebras with non-nilpotent locally nilpotent radicals.