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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 aα+bβ+cγ 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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Cite

BibTeXRIS
BibTeX
@misc{avetisyan2026uniqueness,
  title = {{Uniqueness of universal quantum dimensions}},
  author = {M. Y. Avetisyan and R. L. Mkrtchyan},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30012},
  eprint = {2608.30012},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30012},
}
RIS
TY  - UNPB
TI  - Uniqueness of universal quantum dimensions
AU  - M. Y. Avetisyan
AU  - R. L. Mkrtchyan
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.30012
UR  - https://arxiv.org/abs/2608.30012
AB  - 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 aα+bβ+cγ 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.
ER  -