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- W2964136410 abstract "Abstract The quantum co-ordinate algebra Aq(g) associated to a Kac–Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional irreducible Uq(g) modules. In this paper, we investigate whether an analogous result is true when q=0. We classify crystal bases as coalgebras over a comonadic functor on the category of pointed sets and encode the monoidal structure of crystals into a bicomonadic structure. In doing this, we prove that there is no coalgebra in the category of pointed sets whose comodules are equivalent to crystal bases. We then construct a bialgebra over Z whose based comodules are equivalent to crystals, which we conjecture is linked to Lusztig’s quantum group at v=∞." @default.
- W2964136410 created "2019-07-30" @default.
- W2964136410 creator A5079746031 @default.
- W2964136410 date "2019-03-20" @default.
- W2964136410 modified "2023-09-24" @default.
- W2964136410 title "A categorical reconstruction of crystals and quantum groups at q = 0" @default.
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- W2964136410 doi "https://doi.org/10.1093/qmath/haz001" @default.
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