Unicity for representations of the Kauffman bracket skein algebra
Unicity for representations of the Kauffman bracket skein algebra
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DOI：
10.1007/s00222-018-0833-x
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发表时间：
2017-07
影响因子：
3.1
通讯作者：
C. Frohman;J. Kania-Bartoszyńska;Thang T. Q. Lê
中科院分区：
文献类型：
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作者：
C. Frohman;J. Kania-Bartoszyńska;Thang T. Q. Lê
本文解决了Bonahon和Wong关于在所有单位根上的所有定向有限型曲面的Kauffman括号串代数的唯一性猜想。这个证明是一般唯一性定理的一个推论，该定理说代数闭域k上的素仿射代数的不可约表示，即在其中心上的模的不可约表示，一般由它们的中心特征标来分类。刻画了任意可定向曲面在单位根上的Kauffman括号skein代数的中心，证明了skein代数是其中心上的模的逆生成.它表明，对任何可定向表面的中心的绞代数在任何根的单位是坐标环的仿射代数簇。
This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affinek-algebra over an algebraically closed fieldk, that is finitely generated as a module over its center, are generically classified by their central characters. The center of the Kauffman bracket skein algebra of any orientable surface at any root of unity is characterized, and it is proved that the skein algebra is finitely generated as a module over its center. It is shown that for any orientable surface the center of the skein algebra at any root of unity is the coordinate ring of an affine algebraic variety.