Differential calculus on Hopf--Galois extension via the Durdević braiding
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914578529517568 |
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| author | Bhattacharjee, Arnab |
| author_facet | Bhattacharjee, Arnab |
| contents | We introduce a class of right $H$--covariant first--order differential calculi on principal comodule algebras generated by the Durdević braiding $σ$ and a chosen vertical ideal. Starting from the universal calculus, a strong connection, and a right $H$--colinear splitting map, we construct $σ$--generated differential calculi and prove their existence for arbitrary principal comodule algebras. We show that, in this framework, universal vertical maps and connection $1$--forms descend naturally to the quotient calculus under suitable compatibility conditions. We further develop a functorial formulation of $σ$--generated calculi and establish a universal factorization property for the associated quotient calculi. Finally, we present explicit examples arising from quantum projective spaces and quantum lens spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17760 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Differential calculus on Hopf--Galois extension via the Durdević braiding Bhattacharjee, Arnab Quantum Algebra Primary: 16T05, Secondary: 58B32, 81R50 We introduce a class of right $H$--covariant first--order differential calculi on principal comodule algebras generated by the Durdević braiding $σ$ and a chosen vertical ideal. Starting from the universal calculus, a strong connection, and a right $H$--colinear splitting map, we construct $σ$--generated differential calculi and prove their existence for arbitrary principal comodule algebras. We show that, in this framework, universal vertical maps and connection $1$--forms descend naturally to the quotient calculus under suitable compatibility conditions. We further develop a functorial formulation of $σ$--generated calculi and establish a universal factorization property for the associated quotient calculi. Finally, we present explicit examples arising from quantum projective spaces and quantum lens spaces. |
| title | Differential calculus on Hopf--Galois extension via the Durdević braiding |
| topic | Quantum Algebra Primary: 16T05, Secondary: 58B32, 81R50 |
| url | https://arxiv.org/abs/2601.17760 |