Department of Mathematics

Seminar in Cluster algebras

  •  Vijay Higgins, Michigan State University
  •  Sp(4) stated skein algebras
  •  10/10/2022
  •  3:00 PM - 4:00 PM
  •  C204A Wells Hall
  •  Linhui Shen (shenlin1@msu.edu)

Skein algebras are spanned by webs or links in a thickened surface subject to skein relations. When the skein relations are the Kauffman bracket relations associated to SL(2), they provide a diagrammatic way to encode cluster algebras, as shown by Muller, and also quantum groups, as shown by Costantino and Le. In this talk, we will explore a construction of a basis for the stated skein algebra for Sp(4) which is built from Kuperberg's web relations along with extra skein relations along the boundary of the surface. We will use the basis to obtain results about the structure of the skein algebra, relating it to the quantum group associated to Sp(4). We will also recover Kuperberg's result about the Sp(4) web category.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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