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arXiv · 2608.30012

Uniqueness of universal quantum dimensions

M. Y. Avetisyan·R. L. Mkrtchyan
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Abstract

We prove, under some assumptions, the uniqueness of universal quantum dimension formulae. We first show that the quantum dimensions of classical algebras have a specific form that can be represented universally, in Vogel's sense, as the product/ratio of q-dimension factors with arguments $a\alpha+b\beta+c\gamma$ where $c=0, 1, 2$ and $a, b$ are integers. On this basis, we derive simple uniqueness criteria, according to which all known universal quantum dimensions are unique.

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M. Y. Avetisyan, R. L. Mkrtchyan. 2026-08-30. Uniqueness of universal quantum dimensions. https://arxiv.org/abs/2608.30012

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