## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 6 (2019), 919-940.

### Truncated path algebras and Betti numbers of polynomial growth

#### 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 $βi(S)=ik$ for $2≤k≤4$ and provide a result of the existence of algebras where $βi(S)$ 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.

#### Article information

Source
Involve, Volume 12, Number 6 (2019), 919-940.

Dates
Revised: 24 May 2018
Accepted: 31 January 2019
First available in Project Euclid: 13 August 2019

https://projecteuclid.org/euclid.involve/1565661764

Digital Object Identifier
doi:10.2140/involve.2019.12.919

Mathematical Reviews number (MathSciNet)
MR3990789

Zentralblatt MATH identifier
07116061

#### Citation

Coopergard, Ryan; Purin, Marju. Truncated path algebras and Betti numbers of polynomial growth. Involve 12 (2019), no. 6, 919--940. doi:10.2140/involve.2019.12.919. https://projecteuclid.org/euclid.involve/1565661764

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