对合代数的可积表示与Ore局部化
Integrable representations of involutive algebras and Ore localization
摘要：
设$\mathcal A$是一个具有对合$(\cdot)^\dagger$的酉代数，并假定由形式$1 + a^\dagger a$的元素生成的乘法集$\mathcal S\subseteq \mathcal A$满足Ore条件.我们证明：（i）$\mathcal A$的循环表示允许可积扩展（作用于可能更大的希尔伯特空间），（ii）$\mathcal A$的可积表示与Ore局部化$\mathcal A\mathcal S^{-1}$的表示（我们证明它是一个对合代数）是双射的.这第二个结果是一个有限的逆定理井上断言，表示对称对合代数是可积的。
英文摘要：
Let $\mathcal A$ be a unital algebra equipped with an involution $(\cdot)^\dagger$, and suppose that the multiplicative set $\mathcal S\subseteq \mathcal A$ generated by the elements of the form $1 + a^\dagger a$ satisfies the Ore condition. We prove that: (i) Cyclic representations of $\mathcal A$ admit an integrable extension (acting on a possibly larger Hilbert space), and (ii) Integrable representations of $\mathcal A$ are in bijection with representations of the Ore localization $\mathcal A\mathcal S^{-1}$ (which we prove to be an involutive algebra). This second result is a limited converse to a theorem by Inoue asserting that representations of symmetric involutive algebras are integrable.
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