Dual Presentation and Linear Basis of Temperley-lieb Algebra
نویسنده
چکیده
The braid groups map homomorphically into the Temperley-Lieb algebras. Recently, Zinno showed that the homomorphic images of the simple elements arising from the dual presentation of the braid groups form a basis for the vector space underlying the Temperley-Lieb algebras. We give a simple geometric proof of his theorem, using a new presentation of the Temperley-Lieb algebras that corresponds to the dual presentation of the braid groups.
منابع مشابه
Dual Presentation and Linear Basis of the Temperley-lieb Algebras
The braid groups map homomorphically into the Temperley-Lieb algebras. Recently, Zinno showed that the homomorphic images of the simple elements arising from the dual presentation of the braid groups form a basis for the vector space underlying the Temperley-Lieb algebras. We give a simple geometric proof of his theorem, using a new presentation of the Temperley-Lieb algebras that corresponds t...
متن کاملA pr 2 00 6 DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY - LIEB
The braid group Bn maps homomorphically into the TemperleyLieb algebra TLn. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group Bn form a basis for the vector space underlying the Temperley-Lieb algebra TLn. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual ...
متن کاملar X iv : q - a lg / 9 71 20 46 v 2 2 8 Se p 19 98 Web bases for sl ( 3 ) are not dual canonical
or its invariant space Inv(V1 ⊗ V2 ⊗ . . .⊗ Vn). The quantum group Uq(g) has representations and vector spaces of invariants which generalize these, and one can also study their bases, with or without the intention of specializing to q = 1. (For simplicity, we will usually consider Uq(g) as an algebra over C(q ), and we will only occassionally mention Z[q] as a ground ring.) Lusztig’s remarkabl...
متن کاملOn One Algebra of Temperley–Lieb Type
An algebra generated by projections with relations of Temperley–Lieb type is considered. Knowledge of Gröbner basis of the ideal allows to find a linear basis of the algebra. Some questions of representation theory for this algebra were studied in [13]. Obtained in the present paper are the additional relations, which hold in all finite-dimensional irreducible ∗-representations, although they d...
متن کاملDiagonal Temperley-lieb Invariants and Harmonics
In the context of the ring Q[x,y], of polynomials in 2n variables x = x1, . . . , xn and y = y1, . . . , yn, we introduce the notion of diagonally quasisymmetric polynomials. These, also called diagonal Temperley-Lieb invariants, make possible the further introduction of the space of diagonal Temperley-Lieb harmonics and diagonal Temperley-Lieb coinvariant space. We present new results and conj...
متن کامل