Integral quantum cluster structures
| Autor: | Ken R. Goodearl, Milen Yakimov |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Weyl group
Pure mathematics General Mathematics 010102 general mathematics Unipotent 01 natural sciences Cluster algebra Nilpotent symbols.namesake 0103 physical sciences Cluster (physics) symbols Canonical form 010307 mathematical physics 0101 mathematics Element (category theory) Quantum Mathematics |
| Zdroj: | Duke Mathematical Journal. 170 |
| ISSN: | 0012-7094 |
| DOI: | 10.1215/00127094-2020-0061 |
| Popis: | We prove a general theorem for constructing integral quantum cluster algebras over Z[q±1/2], namely, that under mild conditions the integral forms of quantum nilpotent algebras always possess integral quantum cluster algebra structures. These algebras are then shown to be isomorphic to the corresponding upper quantum cluster algebras, again defined over Z[q±1/2]. Previously, this was only known for acyclic quantum cluster algebras. The theorem is applied to prove that, for every symmetrizable Kac–Moody algebra g and Weyl group element w, the dual canonical form Aq(n+(w))Z[q±1] of the corresponding quantum unipotent cell has the property that Aq(n+(w))Z[q±1]⊗Z[q±1]Z[q±1/2] is isomorphic to a quantum cluster algebra over Z[q±1/2] and to the corresponding upper quantum cluster algebra over Z[q±1/2]. |
| Databáze: | OpenAIRE |
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