A Quasi-Triangular Hopf Structure Derived from the Burchnall–Chaundy C*-Algebra

The Burchnall–Chaundy algebra is a commutative algebra of formal pseudodifferential operators that is instrumental for constructing Lax pairs. It has been shown that via an operator-theory modification of the Sato correspondence, there is an associated C*-algebra: the Burchnall–Chaundy C*-algebra. Commencing with the relationship between a Baxter Lie algebra and Lax pairs, it is shown that the Burchnall–Chaundy C*-algebra naturally leads to an associated quasi-triangular Hopf C*-algebra when the latter is viewed initially in the category of locally compact quantum semigroups. atics Subject Classification (2010): 47A05 (47B10 53B10).