Journal article
Restriction and induction of indecomposable modules over the Temperley-Lieb algebras
J Belletête, D Ridout, Y Saint-Aubin
Journal of Physics A Mathematical and Theoretical | IOP PUBLISHING LTD | Published : 2018
Abstract
Both the original Temperley-Lieb algebras TLn and their dilute counterparts dTLn form families of filtered algebras: TLn ⊂ TL+1n and dTLnn ⊂ dTLn+1, for all n≥0. For each such inclusion, the restriction and induction of every finite-dimensional indecomposable module over TLn (or dTLn) is computed. To accomplish this, a thorough description of each indecomposable is given, including its projective cover and injective hull, some short exact sequences in which it appears, its socle and head, and its extension groups with irreducible modules. These data are also used to prove the completeness of the list of indecomposable modules, up to isomorphism. In fact, two completeness proofs are given - t..
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Awarded by Horizon 2020 Framework Programme
Funding Acknowledgements
We thank Ingo Runkel for a careful reading of the manuscript. DR also thanks Gus Lehrer for a discussion concerning cellular approaches to classifying indecomposable modules, and Tony Licata for helpful pointers on quivers and zigzag algebras. JB holds scholarships from Fonds de recherche Nature et technologies (Quebec) and from the Faculte des etudes superieures et postdoctorales de l'Universite de Montreal, and is supported by the European Research Council (advanced grant NuQFT), DR's research is partially funded by the Australian Research Council Discovery Projects DP1093910 and DP160101520, and YSA holds a grant from the Natural Sciences and Engineering Research Council of Canada. This support is gratefully acknowledged.