Strict comparison in reduced group C*-algebras

• 成果类型: Article
• 署名作者: Amrutam, Tattwamasi; Gao, David; Elayavalli, Srivatsav Kunnawalkam; Patchell, Gregory
• 署名单位: Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of California System; University of California San Diego
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01366-5
• 发表日期: 2025
• 页码: 639-657
• 关键词: rapid decay property; stable rank; HYPERBOLIC GROUPS; K-THEORY; dimension; projections; COHOMOLOGY; SUBGROUPS; centroids; PRODUCTS

摘要

We prove that for every n is an element of N such that n >= 2, the reduced group C*-algebras of the countable free groups Cr*(Fn) have strict comparison. Our method works in a general setting: for every finitely generated acylindrically hyperbolic group G with trivial finite radical and the rapid decay property, we have Cr*(G) have strict comparison. This work also has several applications in the theory of C*-algebras including: resolving Leonel Robert's selflessness problem for Cr*(G) uniqueness of embeddings of the Jiang-Su algebra Z up to approximate unitary equivalence into Cr*(G); full computations of the Cuntz semigroup of Cr*(G) and future directions in the C*-classification program.