Free path groupoid grading on Leavitt path algebras
Mathematics - Rings and Algebras | Mathematics - Operator Algebras | 16W50, 16W55, 16G99
arxiv: Mathematics::K-Theory and Homology | Mathematics::Commutative Algebra | Mathematics::Category Theory | Mathematics::Operator Algebras | Mathematics::Rings and Algebras
In this work we realize Leavitt path algebras as partial skew groupoid rings. This yields a free path groupoid grading on Leavitt path algebras. Using this grading we characterize free path groupoid graded isomorphisms of Leavitt path algebras that preserves generators.