Gröbner–Shirshov Bases for Temperley–Lieb Algebras of Type <i>F</i>

Abstract

For the Temperley–Lieb algebras of type Fn with n≥4, we construct their Gröbner–Shirshov bases. Explicitly, the corresponding finite sets consisting of the standard monomials of type Fn, which are exactly the fully commutative elements of Fn, are enumerated when n = 4, 5, and 6.

Keywords

• Gröbner–Shirshov basis
• Temperley–Lieb algebra
• fully commutative element