We prove that both stated skein algebras and their reduced versions at odd roots of unity are almost-Azumaya and compute the rank of a reduced stated skein algebra over its center, extending a theorem of Frohman, Kania-Bartoszynska and Le to the case of open surfaces. We deduce that generic irreducible representations of the reduced stated skein algebras are of quantum Teichmuller type and, conversely, that generic quantum Teichmuller type representations are irreducible.

中文翻译：

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表示简化的绞线代数的唯一性

我们证明了陈述的绞线代数及其在奇数根的简化版本几乎是 Azumaya 并计算了简化的陈述绞线代数在其中心上的秩，将 Frohman、Kania-Bartoszynska 和 Le 的定理扩展到开的情况表面。我们推导出简化的陈述绞线代数的通用不可约表示是量子 Teichmuller 类型的，相反，通用量子 Teichmuller 类型表示是不可约的。