Triangular decomposition of skein algebras

By Thang T. Q. Lê. Quantum Topology, 2016

67 citations recorded by the source corpus.

By introducing a finer version of the Kauffman bracket skein algebra, we show how to decompose the Kauffman bracket skein algebra of a surface into elementary blocks corresponding to the triangles in an ideal triangulation of the surface. The new skein algebra of an ideal triangle has a simple presentation. This gives an easy proof of the existence of the quantum trace map of Bonahon and Wong. We also explain the relation between our skein algebra and the one defined by Muller, and use it to show that the quantum trace map can be extended to the Muller skein algebra.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/97e39a4f9051b0a3286fbeee39f4bad954493962

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In Geometry and Topology

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Citations in the corpus

Stated skein algebras of surfaces (2019, methodology): “Actually in [Le2] the reduced stated skein algebra was not introduced, instead a direct algebra homomorphism from S (P3) to T′ is constructed.”
The finiteness conjecture for skein modules (2019, background): “We see that this is exactly the stated skein algebra introduced in [32,63] (see also a related definition of relative skein algebras of [64]).”
Skein algebras of surfaces (2016, methodology): “rA 1s:(Later, Muller constructed an embedding of his skein algebra Sk qpFqfor BF ˘H;into a quantum torus. Various simplications and enhancements of Bonahon-Wang and Muller work were obtained by L^e, [Le1, Le2, Le3].) 4 JOZEF H. PRZYTYCKI, ADAM S. SIKORA Additionally, [CM] proved that the skein algeb”