Spectral Fusion Deformations for Locally Compact Quantum Groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909993007054848 |
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| author | Sangha, Amandip |
| author_facet | Sangha, Amandip |
| contents | We develop a deformation framework for $C^*$-algebras equipped with a coaction of a locally compact quantum group, formulated intrinsically at the level of spectral subspaces determined by the coaction. The construction is defined algebraically on a finite spectral core and extended by continuity to a natural Fréchet $*$-algebra completion under mild analytic regularity assumptions.
Deformations are governed by scalar fusion data assigning phases to fusion channels of irreducible corepresentations. Associativity and $*$-compatibility are characterized by explicit algebraic identities. The framework recovers a range of known deformation procedures, including Rieffel, Kasprzak, and Drinfeld-type constructions, and also yields genuinely new deformations that do not arise from dual $2$--cocycles or crossed-product methods.
At the $C^*$-level, we identify a minimal reduced setting in which the deformed algebra admits a canonical completion, formulated in terms of boundedness of the deformed left regular action on the Haar--GNS space. This separates algebraic coherence from analytic implementability and clarifies the precise role of higher-order fusion data in deformation theory for locally compact quantum groups. In particular, the framework exhibits explicit associator-level deformations governed by fusion $3$--cocycles that cannot arise from any dual $2$--cocycle or crossed-product construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Fusion Deformations for Locally Compact Quantum Groups Sangha, Amandip Operator Algebras Functional Analysis K-Theory and Homology Quantum Algebra We develop a deformation framework for $C^*$-algebras equipped with a coaction of a locally compact quantum group, formulated intrinsically at the level of spectral subspaces determined by the coaction. The construction is defined algebraically on a finite spectral core and extended by continuity to a natural Fréchet $*$-algebra completion under mild analytic regularity assumptions. Deformations are governed by scalar fusion data assigning phases to fusion channels of irreducible corepresentations. Associativity and $*$-compatibility are characterized by explicit algebraic identities. The framework recovers a range of known deformation procedures, including Rieffel, Kasprzak, and Drinfeld-type constructions, and also yields genuinely new deformations that do not arise from dual $2$--cocycles or crossed-product methods. At the $C^*$-level, we identify a minimal reduced setting in which the deformed algebra admits a canonical completion, formulated in terms of boundedness of the deformed left regular action on the Haar--GNS space. This separates algebraic coherence from analytic implementability and clarifies the precise role of higher-order fusion data in deformation theory for locally compact quantum groups. In particular, the framework exhibits explicit associator-level deformations governed by fusion $3$--cocycles that cannot arise from any dual $2$--cocycle or crossed-product construction. |
| title | Spectral Fusion Deformations for Locally Compact Quantum Groups |
| topic | Operator Algebras Functional Analysis K-Theory and Homology Quantum Algebra |
| url | https://arxiv.org/abs/2601.08688 |