TL;DR
This paper studies the structure of the stated skein algebra at roots of unity, providing a simple description of its center and calculating its dimension over the center, advancing understanding in quantum topology.
Contribution
It offers a clear description of the center of the stated skein algebra and computes its dimension over the center, enhancing the algebra's structural understanding.
Findings
The center of the stated skein algebra is explicitly described.
The dimension of the algebra over its center is calculated.
The results apply when the quantum parameter is a root of unity.
Abstract
The stated skein algebra is a generalization of the Kauffman bracket skein algebra introduced in the study of quantum trace maps. When the quantum parameter is a root of unity, the stated skein algebra has a big center and is finitely generated as a module over the center. We give the center a simple description and calculate the dimension over center of the stated skein algebra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum Computing Algorithms and Architecture · Neural Networks and Reservoir Computing