Classification conjectures for Leavitt path algebras

Abstract

The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and $C^{\ast }$-algebras where the major classification programs have been a domain of intense research in the last 50 years. In this survey article, we gather together current lines of research in the classification of Leavitt path algebras, questions, conjectures, and some of the results about them that have been obtained so far.

arXiv commentFinal version

References in corpus (9)

• Graded Steinberg algebras and their representations
• K-theoretic duality for shifts of finite type
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Tensor products of Leavitt path algebras
• $\ast$-isomorphism of Leavitt path algebras over $\mathbb{Z}$
• Shift equivalences through the lens of Cuntz-Krieger algebras
• Homotopy classification of Leavitt path algebras
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Cited by in corpus (2)

• The socle of subshift algebras, with applications to subshift conjugacy
• Higher-rank graphs and the graded $K$-theory of Kumjian-Pask algebras