Cyclotomic blob algebra and its representation theory
نویسندگان
چکیده
منابع مشابه
The Blob Algebra and the Periodic Temperley-lieb Algebra
We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the ‘blob’ algebra (the reason for the name will become obvious shortly!). We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the period...
متن کاملThe representation theory of cyclotomic Temperley-Lieb algebras
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 nonstandard Hecke algebra Ȟr was defined in [11] to study the Kronecker problem. We study a quotient Ȟr,2 of Ȟr , called the nonstandard Temperley-Lieb algebra, which is simpler than Ȟr. It is defined to be the subalgebra of Hr,2⊗Hr,2 generated by Pi := C ′ i ⊗C ′ i +Ci ⊗Ci, i ∈ [r− 1], where Hr,2 is the Temperley-Lieb algebra and C i and Ci are Kazhdan-Lusztig basis elements. We give a com...
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We describe the complete set of pairwise non-isomorphic irreducible modules Sα over the algebra R = k〈x, y〉/(xy − yx − y ), and the rule how they could be glued to indecomposables. Namely, we show that Ext1k(Sα, Sβ) = 0, if α 6= β. Also the set of all representations is described subject to the Jordan normal form of Y . We study then properties of the image algebras in the endomorphism ring. Am...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2006
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2005.06.011