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離散数理モデリングセミナー
過去の記録 ～04/26｜次回の予定｜今後の予定 04/27～
| 担当者 | 時弘哲治, ウィロックス ラルフ |
|---|
2021年06月30日(水)
17:15-18:45 オンライン開催
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Joe PALLISTER 氏 (千葉大学)
Affine A and D cluster algebras: Dynamical systems, triangulated surfaces and friezes (English)
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Joe PALLISTER 氏 (千葉大学)
Affine A and D cluster algebras: Dynamical systems, triangulated surfaces and friezes (English)
[ 講演概要 ]
We first review the dynamical systems previously obtained for affine A and D type cluster algebras, given by the "cluster map", and the periodic quantities found for these systems. Then, by viewing the clusters as triangulations of appropriate surfaces, we show that all cluster variables either:
(i) Appear after applying the cluster map
(ii) Can be written as a determinant function of the periodic quantities.
Finally we show that the sets of cluster variables (i) and (ii) both form friezes.
We first review the dynamical systems previously obtained for affine A and D type cluster algebras, given by the "cluster map", and the periodic quantities found for these systems. Then, by viewing the clusters as triangulations of appropriate surfaces, we show that all cluster variables either:
(i) Appear after applying the cluster map
(ii) Can be written as a determinant function of the periodic quantities.
Finally we show that the sets of cluster variables (i) and (ii) both form friezes.
