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This research explores the relationships between quantum group knot invariants at roots of unity and their representation in topological quantum field theories.

July 26, 2026Open Access

Quantum Group Knot Invariants at Roots of Unity and Root Lattice TQFTs — E8 Intelligence Research

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This research explores the relationships between quantum group knot invariants at roots of unity and their representation in topological quantum field theories.
Evaluated quantum group representations at roots of unity, specifically for various root systems like E8.
Investigated fusion rules governed by Weyl group symmetry in relation to knot invariants.
Analyzed periodic patterns in quantum integers and ratios linking to the golden ratio.
Found finite-dimensional representations yield new link invariants linked to root system lattices.
Demonstrated that quantum integers reduce to simpler forms at specific roots of unity, revealing periodicity.
Identified connections between trigonometric ratios and the golden ratio for certain values of root order.

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Randomized trial examines quantum group knot invariants and their implications for root systems, suggesting new insights for TQFTs.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a65a6b5d3aea3239cd77e46 https://doi.org/10.5281/zenodo.21503529

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Quantum Group Knot Invariants at Roots of Unity and Root Lattice TQFTs — E8 Intelligence Research

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Quantum Group Knot Invariants at Roots of Unity and Root Lattice TQFTs — E8 Intelligence Research

Key Points

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Implication

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