An explicit projective bimodule resolution of a Leavitt path algebra

TL;DR

This paper constructs an explicit projective bimodule resolution for Leavitt path algebras of row-finite quivers and proves they have Hochschild cohomological dimension at most one, indicating quasi-freeness.

Contribution

It provides the first explicit bimodule resolution for Leavitt path algebras and establishes their Hochschild cohomological dimension as at most one.

Findings

Leavitt path algebra of a row-finite quiver has Hochschild cohomological dimension ≤ 1

Constructs an explicit projective bimodule resolution

Shows Leavitt path algebra is quasi-free in the sense of Cuntz-Quillen

Abstract

We construct an explicit projective bimodule resolution for the Leavitt path algebra of a row-finite quiver. We prove that the Leavitt path algebra of a row-countable quiver has Hochschild cohomolgical dimension at most one, that is, it is quasi-free in the sense of Cuntz-Quillen. The construction of the resolution relies on an explicit derivation of the Leavitt path algebra.