There exists a multiplicative homomorphism from the braid group (Formula presented.) on k + 1 strands to the Temperley–Lieb algebra TLk. Moreover, the homomorphic images in TLk of the simple elements form a basis for the vector space underlying TLk. In analogy with the case of Bk, there exists a multiplicative homomorphism from the structure group G(X, r) of a non-degenerate, involutive set-theoretic solution (X, r), with (Formula presented.), to an algebra, which extends to a homomorphism of algebras. We construct a finite basis of the underlying vector space of the image of G(X, r) using the Garsideness properties of G(X, r).
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- Coxeter-like quotient groups
- Garside groups and monoids
- set-theoretic solutions of the quantum Yang-Baxter equation
ASJC Scopus subject areas
- Algebra and Number Theory