Dual Presentation and Linear Basis of the Temperley-lieb Algebras
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 Temperley-lieb Algebra
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 ...
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A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint ...
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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...
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