Integrable models from singly generated planar algebras

Not all planar algebras can encode the algebraic structure of a Yang--Baxter integrable model described in terms so-called homogeneous transfer operator. In family subfactor algebras, we focus on ones known as singly generated and find that only such underlying models are relation algebras. According to result Liu, there three algebras: well-known Fuss--Catalan Birman--Wenzl--Murakami addition one more which refer Liu algebra. The underlie models, show algebra likewise admits Baxterisation. We also operator describing underlied by is polynomialisable, meaning it polynomial spectral-parameter-independent element