Data
- Title: Möbius strip diagram algebras
- Authors: Daniel W. Collison and Daniel Tubbenhauer
- Status: preprint. Last update: Thu, 12 Feb 2026 05:17:51 UTC
- ArXiv link: https://arxiv.org/abs/2602.11591
Abstract
We introduce Möbius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and Möbius 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.
A few extra words
Here is the Möbius relation:
