Growth and Structure of Leavitt Path Algebras

We prove results for Leavitt path algebras with coefficients in a unital commutative ring most of which are new for field coefficients also. In particular, we show that the ideal lattice of a Leavitt path algebra embeds into the ideal lattice of the path algebra of the same digraph. As a consequence we provide a convenient alternative to the Graded Uniqueness Theorem, which does not require the homomorphism to be graded. We construct new bases for Leavitt path algebras of polynomial growth and give a formula for their Gelfand-Kirillov dimensions in terms of their digraphs. We also give a generalization of the reduction algorithm which has proven useful in various applications.