M\"obius Strip Diagram Algebras
Representation Theory
2026-02-13 v1 Group Theory
Abstract
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram category with a linear quotient of a nonorientable two-dimensional cobordism category. Finally, we develop the associated cell theory and use it to classify the simple modules and compute dimensions in a range of cases.
Cite
@article{arxiv.2602.11591,
title = {M\"obius Strip Diagram Algebras},
author = {D. W. Collison and D. Tubbenhauer},
journal= {arXiv preprint arXiv:2602.11591},
year = {2026}
}
Comments
30 pages, many figures, comments welcome