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arXiv · 2602.11591

M\"obius Strip Diagram Algebras

D. W. Collison·D. Tubbenhauer
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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.

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D. W. Collison, D. Tubbenhauer. 2026-02-12. M\"obius Strip Diagram Algebras. https://arxiv.org/abs/2602.11591

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