2025/10/17 by Björn Malte Schäfer, Schäfer, Björn
Computer Science · Mathematics · #46L35 #47C15 #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2510.15586
openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
We study C*-algebras generated by two partitions of unity with orthogonality relations governed by hypercubes Qn for n ∈ ℕ ∖ \0\. These "hypercube C*-algebras'' are special cases of bipartite graph C*-algebras which have been investigated by the author in a previous work. We prove that the hypercube C*-algebras C^∗(Qn) are subhomogeneous and obtain an explicit description as algebra of continuous functions from a standard simplex into a finite-dimensional matrix algebra with suitable boundary conditions. Thus, we generalize Pedersen's description of the universal unital C*-algebra C^∗(p,q) of two projections. We use our results to prove that any 2 × 4 "magic isometry'' matrix can be filled up to a 4 × 4 "magic unitary'' matrix. This answers a question from Banica, Skalski and Sołtan.