Resumen

In joint work with Murad Özaydın we provide a complete answer to the question "When is a quotient  of a Leavitt path algebra  isomorphic to a Leavitt path algebra?" in terms of the interaction of the kernel of the quotient homomorphism with the cycles of the digraph. We define a stratification and a parametrization of the ideal space of a Leavitt path algebra (initially in terms of the digraph, later algebraically) and show that a generic quotient of a Leavitt path algebra  is a Leavitt path algebra. Along the way we show that the lattice of graded ideals of a Leavitt path algebra is a Morita invariant, hence independent of the grading. Contrary to most algebraic properties of Leavitt path algebras, our criterion for a quotient to be isomorphic to a Leavitt path algebra is not independent of the field of coefficients.

This study was supported by Scientific and Technological Research Council of Türkiye.

 

 
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