The Kauffman Skein Algebra of the Torus. (14th March 2022)

• Record Type: Journal Article
• Authors: Morton, Hugh; Pokorny, Alex; Samuelson, Peter
• Is Part Of: International mathematics research notices. Volume 2023:Number 1(2023)
• Page Start: 855
• Page End: 900
• Publication Date: 2022-03-14
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnac025
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We give a presentation of the Kauffman (BMW) skein algebra of the torus. This algebra is the "type $BCD$ " analogue of the Homflypt skein algebra of torus, which was computed in earlier work of the 1st and 3rd authors [17 ]. This suggests the existence of a "type $BCD$ " version of the Hall algebra of an elliptic curve [4 ]. In the appendix, we show this presentation is compatible with the Frohman–Gelca description of the Kauffman bracket (Temperley–Lieb) skein algebra of the torus [12 ].