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- W2964316107 abstract "Let k be an arbitrary field and let q∈k∖{0}. In this paper we use the known tilting theory for the quantum group Uq(sl2) to obtain the dimensions of simple modules for the Temperley–Lieb algebras TLn(q+q−1) and related algebras over k. Our main result is an algorithm which calculates the dimensions of simple modules for these algebras. We take advantage of the fact that TLn(q+q−1) is isomorphic to the endomorphism ring of the n'th tensor power of the natural 2-dimensional module for the quantum group for sl2. This algorithm is easy when the characteristic is 0 and more involved in positive characteristic. We point out that our results for the Temperley–Lieb algebras contain a complete description of the simple modules for the Jones quotient algebras. Moreover, we illustrate how the same results lead to corresponding information about simple modules for the BMW-algebras with special parameters and other algebras closely related with endomorphism algebras of families of tilting modules for Uq(sl2)." @default.
- W2964316107 created "2019-07-30" @default.
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- W2964316107 date "2019-02-01" @default.
- W2964316107 modified "2023-10-18" @default.
- W2964316107 title "Simple modules for Temperley–Lieb algebras and related algebras" @default.
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- W2964316107 doi "https://doi.org/10.1016/j.jalgebra.2018.10.035" @default.
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