Truncated path algebras and Betti numbers of polynomial growth

Coopergard, Ryan; Purin, Marju

doi:10.2140/involve.2019.12.919

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

This article is available for purchase or by subscription. See below.

Truncated path algebras and Betti numbers of polynomial growth

Ryan Coopergard and Marju Purin

Vol. 12 (2019), No. 6, 919–940

DOI: 10.2140/involve.2019.12.919

Abstract

We investigate a class of truncated path algebras in which the Betti numbers of a simple module satisfy a polynomial of arbitrarily large degree. We produce truncated path algebras where the $i$ -th Betti number of a simple module $S$ is $β_{i} (S) = i^{k}$ for $2 \leq k \leq 4$ and provide a result of the existence of algebras where $β_{i} (S)$ is a polynomial of degree 4 or less with nonnegative integer coefficients. In particular, we prove that this class of truncated path algebras produces Betti numbers corresponding to any polynomial in a certain family.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 3.237.27.159 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords

finite-dimensional algebra, Betti number, path algebra, quiver

Mathematical Subject Classification 2010

Primary: 16P90

Secondary: 16P10, 16G20

Milestones

Received: 23 December 2016

Revised: 24 May 2018

Accepted: 31 January 2019

Published: 3 August 2019

Communicated by Kenneth S. Berenhaut

Authors

Ryan Coopergard
Department of Mathematics University of Minnesota - Twin Cities Minneapolis, MN United States

Marju Purin
Department of Mathematics, Statistics, and Computer Science St. Olaf College Northfield, MN United States

Vol. 12, No. 6, 2019