A pr 2 00 6 DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY - LIEB
نویسندگان
چکیده
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 presentation of braid groups, and then give a simple geometric proof for Zinno’s theorem, using the interpretation of simple elements as non-crossing partitions.
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...
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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...
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