Truncated path algebras and Betti numbers of polynomial growth

Abstract

Path Algebras and Betti Numbers with Polynomial Growth. Preliminary report. In this talk, we will introduce a class of truncated path algebras in which the Betti numbers of a simple module satisfy a polynomial of arbitrarily large degree. We will give examples of such algebras where the i Betti number of a simple module S is βi(S) = i k for 2 ≤ k ≤ 4 and provide a method for constructing truncated path algebras where βi(S) is a polynomial of degree four or less with nonnegative integer coefficients. In particular, we prove that algebras in this class can produce Betti numbers corresponding to any polynomial in a certain family. (Received September 19, 2016)