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A generalization of the Temperley-Lieb algebra from restricted quantum sl2

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OAS - Operator algebras: subfactors and their applications

The Temperley-Lieb algebra was introduced in relation to lattice models in statistical mechanics, before being rediscovered in the standard invariant of subfactors. Alternatively, the Temperley-Lieb algebra can be constructed as the centralizer of the quantum group Uq(sl2). Recent work in logarithmic conformal field theory has brought interest to a restricted version of this quantum group. We generalize the Temperley-Lieb construction to the restricted case, describing generators and a number of relations, then describe morphisms between modules, including a conjecture for the formula for projections onto indecomposable modules.





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