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by A Berenstein, A Zelevinsky

Venue: | Int. Math. Res. Not |

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by
Kyungyong Lee, Li Li, Andrei Zelevinsky
- Selecta Math

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...lready noticed that Proposition 1.8 implies Theorem 1.7(d),(e). This only leaves Theorem 1.7(c), which will be proved in Section 6. Note that our proof of Theorem 1.7(c) is inspired by a recent paper =-=[2]-=-. Our proof of (1.18) uses upper bounds for the supports of greedy elements which we obtain in Section 4 (as usual, the support of a Laurent polynomial x ∈ Z[x±11 , x ±1 2 ] is the set of lattice poin...

by
Arkady Berenstein, Dylan Rupel

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...tion of (2.14) to Ui is an isomorphism Ψ −1 i ◦ηi : Ui→̃kq[Nw]. We conclude the section with the relationship between the twist η : Ui → Ui from Theorem 2.10 and canonical basis in Ui. Recall that in =-=[6]-=- A. Zelevinsky and the first author constructed a triangular basis B(Σ) in the upper cluster algebra U(Σ) for each acyclic quantum seed Σ in Ui and proved that B(Σ) does not depend on the choice of Σ ...

by
Kyungyong Lee, Li Li, Dylan Rupel, Andrei Zelevinsky

"... iv ..."

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...to these algebras. We restrict our attention to rank 2 quantum cluster algebras where we can describe the setup in very concrete terms. We follow (as much as possible) the notation and conventions of =-=[13, 2]-=-. We work in the quantum torus T := Z[v±1]〈X±11 ,X ±1 2 : X2X1 = v 2X1X2〉 (this setup is related to the one in [19] which uses the formal variable q instead of v by setting q = v−2). There are many ch...

by
Arkady Berenstein, Sebastian Zwicknagl
, 2007

"... 2. Main results 6 2.1. Braided symmetric and exterior powers 6 ..."

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