DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)verified 2026-10-22 (gpt-6.1-sol)

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BMW coefficient extension for Dubrovnik parameters

Definition

Let $S = Z [a^{\pm 1}, z, d^{\pm 1}] / (z (d - 1) - (a - a^{- 1}))$ be the universal Dubrovnik coefficient ring. Define the coefficient extension $T = S [q^{\pm 1}] / (q - q^{- 1} - z) .$ Inside $T$ write $z_{B} = q - q^{- 1}$ , $z_{D} = z_{B}$ , $ρ = a$ , and $δ = d$ . These names specify the intended BMW and Dubrovnik parameter images; the compatibility of their coefficient relations is proved separately.

Definition references

Universal Dubrovnik coefficient ring

BMW presentation and parameter symbols

Goodman and Hauschild, Affine Birman–Wenzl–Murakami Algebras and Tangles in the Solid Torus

Poulain d’Andecy, Fusion for the Yang–Baxter Equation and the Braid Group (2020)

Depends on

Used by

Ordinary Dubrovnik tangle skein algebra Definition
BMW relations in the Dubrovnik parameter convention Lemma

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Frederick M. Goodman and Holly Hauschild, Affine Birman–Wenzl–Murakami Algebras and Tangles in the Solid Torus, Definition 3.1 (standard reference, not scraped)
Loïc Poulain d’Andecy, Fusion for the Yang–Baxter Equation and the Braid Group, Winter Braids Lecture Notes 7 (2020), §2.2 (standard reference, not scraped)