Higher-dimensional Temperley-Lieb algebras
نویسندگان
چکیده
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced. MSC-class: 81R50 (primary), 82B20 (secondary).
منابع مشابه
4 N ov 1 99 8 ON REPRESENTATIONS OF AFFINE TEMPERLEY – LIEB ALGEBRAS , II
We study some non-semisimple representations of affine Temperley–Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite dimensional cellular algebra.
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We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras, their partial analogues, Temperley-Lieb algebras, their partial analogues, walled Temperley-Lieb algebras, their partial analogues, partition algebras and their Temperley-Lieb analogues.
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A class of associative algebras called cyclotomic Temperley-Lieb algebras is introduced in terms of generators and relations. They are closely related to the group algebras of complex reflection groups on one hand and generalizations of the usual Temperley-Lieb algebras on the other hand. It is shown that the cyclotomic Temperley-Lieb algebras can be defined by means of labelled Temperley-Lieb ...
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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...
متن کاملDual 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...
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تاریخ انتشار 2007