| Autor: |
Smith, Craig |
| Předmět: |
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| Zdroj: |
Quarterly Journal of Mathematics; Sep2019, Vol. 70 Issue 3, p895-925, 31p |
| Abstrakt: |
The quantum co-ordinate algebra A q (g) associated to a Kac–Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional irreducible U q (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 = ∞ . [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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