Involve: A Journal of Mathematics

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

Truncated path algebras and Betti numbers of polynomial growth

Ryan Coopergard and Marju Purin

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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 2k4 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
Received: 23 December 2016
Revised: 24 May 2018
Accepted: 31 January 2019
First available in Project Euclid: 13 August 2019

Permanent link to this document
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

Subjects
Primary: 16P90: Growth rate, Gelfand-Kirillov dimension
Secondary: 16P10: Finite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} 16G20: Representations of quivers and partially ordered sets

Keywords
finite-dimensional algebra Betti number path algebra quiver

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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