发表机构
Beijing Institute of Mathematical Sciences and Applications; Hetao Institute of Mathematics and Interdisciplinary Sciences（北京数学科学研究所; 河套数学与交叉科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在 Hom-有限幺半范畴中证明可分代数对象的局部 Ocneanu 刚性，通过收缩 Hochschild 上同调获得子代数数量上界，并将 Etingof-Walton 定理改进为 2^(dim_C H)，同时将子因子界从 9^[M:N] 改进到 2^[M:N]。
AI 中文摘要
我们在代数闭域 k 上的 Hom-有限幺半范畴 C 中建立了可分代数对象的局部 Ocneanu 刚性。可分性态射收缩前两个 Hochschild 上同调群，而不需要阿贝尔环境范畴。可分代数结构和来自可分源的同态具有开放的代数群轨道，仿射 Bezout 估计给出有效的有限性结果。对于 Frobenius 子代数，交换关系将源和嵌入数据替换为单个自对偶幂等元。我们证明它们的可分内共轭类在交换轨迹中是开放的，从而对非零环境代数给出 2^(dim_k End_C(X)) 的界；连通性给出实际子代数数量的相同界。作为应用，我们获得 Etingof-Walton 有限性定理的有效形式：复数域上每个有限维半单 Hopf 代数 H 至多有 2^(dim_C H) 个左余理想子代数。在酉设置中，我们在有限指标和有限中心假设下，将 C*-代数和 von Neumann 代数包含的 E-相容中间代数上界限制到酉共轭。对于不可约子因子，这些将 Bakshi-Das-Liu-Ren 的 9^[M:N] 界改进为 2^[M:N]。
英文摘要
We establish local Ocneanu rigidity for separable algebra objects in Hom-finite monoidal categories C over an algebraically closed field k. A separability morphism contracts the first two Hochschild cohomology groups without requiring an abelian ambient category. Separable algebra structures and homomorphisms from separable sources have open algebraic-group orbits, and affine Bezout estimates give effective finiteness results. For Frobenius subalgebras, exchange relations replace the source and embedding data by a single self-dual idempotent. We prove that their separable inner-conjugacy classes are open in the exchange locus, yielding a bound of 2^(dim_k End_C(X)) for nonzero ambient algebras; connectedness gives the same bound on the actual number of subalgebras. As an application, we obtain an effective form of the Etingof-Walton finiteness theorem: every finite-dimensional semisimple Hopf algebra H over the complex numbers has at most 2^(dim_C H) left coideal subalgebras. In the unitary setting, we bound E-compatible intermediates of C*-algebra and von Neumann algebra inclusions up to unitary conjugacy, under finite-index and finite-center hypotheses. For irreducible subfactors, these improve the 9^[M:N] bound of Bakshi-Das-Liu-Ren to 2^[M:N].
Comments35 pages. Added references and clarified the relation to prior work; mathematical results unchanged. An expanded internal version with additional explanations and string diagrams is included as ancillary material. Comments are welcome!
