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for syzygies of string modules over special biserial algebras

Version 0.6.5

Joe Allen (he/him/his)


String modules for special biserial (SB) algebras are represented by string graphs. Many modules related to a given string module, including its syzygy, transpose and vector-space dual and hence Auslander-Reiten translate and inverse translate, are also string modules. These related modules can be calculated combinatorially rather than algebraically. SBStrips implements this functionality in GAP, representing string graphs as objects called strips. It includes some tests for associated properties such as syzygy type, delooping level and weak periodicity.

SBStrips also includes bookkeeping functionality for multisets, which it calls collected lists, and it integrates with (and depends on) the QPA package for quiver algebras and their modules.


© 2020-2021 Joe Allen


I thank my fellow members of "Team Splendid" -- Prof Jeremy Rickard, Dr Simon Peacock, Charley Cummings and Luke Kershaw -- for countless engaging conversations about representation theory, programming and much else besides. In particular I thank my PhD supervisor Jeremy, on whom I inflicted multiple early iterations of SBStrips, for his time and comments and my "big brother" Simon for helping me organise the SBStrips website. This package was much worse before their feedback.

Additionally, I received help understanding GAPDoc from Prof Max Horn and Dr Frank Lübeck, the latter of whom wrote the makedocrel.g file included in this package. I am grateful to them both.


This package was created during the author's doctoral studies at the University of Bristol.


1 Introduction
2 Worked example
3 Mathematical background
4 Strips
5 QPA utilities
6 Miscellaneous utilities
A Example algebras

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