A graded pullback structure of Leavitt path algebras of trimmable graphs

TL;DR

This paper introduces trimmable graphs and demonstrates that their Leavitt path algebras can be expressed as graded pullback algebras, simplifying their structure and analysis.

Contribution

It defines trimmable graphs and establishes a graded-isomorphic pullback structure for their Leavitt path algebras, extending the understanding of algebraic structures related to graph C*-algebras.

Findings

Leavitt path algebra of a trimmable graph is graded-isomorphic to a pullback algebra.

The pullback structure involves simpler Leavitt path algebras and tensor products.

Provides a new structural perspective for analyzing Leavitt path algebras.

Abstract

Motivated by recent results in graph C*-algebras concerning an equivariant pushout structure of the Vaksman-Soibelman quantum odd spheres, we introduce a class of graphs called trimmable. Then we show that the Leavitt path algebra of a trimmable graph is graded-isomorphic to a pullback algebra of simpler Leavitt path algebras and their tensor products.