Quadratic subproduct systems, free products, and their C*-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913799164919808 |
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| author | Arici, Francesca Ge, Yufan |
| author_facet | Arici, Francesca Ge, Yufan |
| contents | Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a finite number of complex quadratic polynomials in noncommuting variables, and describe their Toeplitz and Cuntz--Pimsner algebras. Inspired by the theory of graded associative algebras, we define a free product operation in the category of subproduct systems and show that this corresponds to the reduced free product of the Toeplitz algebras. Finally, we obtain results about the K-theory of the Toeplitz and Cuntz--Pimsner algebras of a large class of quadratic subproduct systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic subproduct systems, free products, and their C*-algebras Arici, Francesca Ge, Yufan Operator Algebras K-Theory and Homology Quantum Algebra Rings and Algebras Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a finite number of complex quadratic polynomials in noncommuting variables, and describe their Toeplitz and Cuntz--Pimsner algebras. Inspired by the theory of graded associative algebras, we define a free product operation in the category of subproduct systems and show that this corresponds to the reduced free product of the Toeplitz algebras. Finally, we obtain results about the K-theory of the Toeplitz and Cuntz--Pimsner algebras of a large class of quadratic subproduct systems. |
| title | Quadratic subproduct systems, free products, and their C*-algebras |
| topic | Operator Algebras K-Theory and Homology Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2504.12843 |