SL_3$绺裂模块的神奇抵消和量子弗罗本尼斯

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-31 DOI:arxiv-2409.00351

Vijay Higgins

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引用次数: 0

摘要

我们构建了一个量子弗罗本尼乌斯图，用于任何取向 3-manifold的$SL_3$绺模块，该模块专一于一个统一根，并通过沿链接穿入某些多项式来描述该图。该同态是 Bonahon-Wong 的 Chebyshev-Frobenius 同态的高阶版本。该策略建立在先前对穿刺面的 $SL_3$ skeinalgebras 的 Frobenius 映射的构造之上，使用了 Parshall-Wang 对量子群 $\mathcal{O}_q(SL_3).$ 的 Frobenius 映射。

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Miraculous cancellations and the quantum Frobenius for $SL_3$ skein modules

We construct a quantum Frobenius map for the $SL_3$ skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynomials along links. The homomorphism is a higher rank version of the Chebyshev-Frobenius homomorphism of Bonahon-Wong. The strategy builds on a previous construction of the Frobenius map for $SL_3$ skein algebras of punctured surfaces, using the Frobenius map of Parshall-Wang for the quantum group $\mathcal{O}_q(SL_3).$

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arXiv - MATH - Quantum Algebra

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