Some Constructions on Quantum Principal Bundles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917237402632192 |
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| author | Moncada, Gustavo Amilcar Saldaña |
| author_facet | Moncada, Gustavo Amilcar Saldaña |
| contents | This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove four statements in the theory of quantum principal bundles:: 1) The universal differential envelope $\ast$--calculus of a matrix (compact) Lie group, for the classical bicovariant $\ast$--First Order Differential Calculus, is the algebra of differential forms. 2) An example of a quantum principal bundle in which the space of base forms is not generated by the base space. 3) The group isomorphism between convolution-invertible maps and covariant left module isomorphisms at the level of differential calculus 4) The way the maps $\{T^V_k \}$ from Remark 3.1 look in differential geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Constructions on Quantum Principal Bundles Moncada, Gustavo Amilcar Saldaña Quantum Algebra 46L87, 58B99 This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove four statements in the theory of quantum principal bundles:: 1) The universal differential envelope $\ast$--calculus of a matrix (compact) Lie group, for the classical bicovariant $\ast$--First Order Differential Calculus, is the algebra of differential forms. 2) An example of a quantum principal bundle in which the space of base forms is not generated by the base space. 3) The group isomorphism between convolution-invertible maps and covariant left module isomorphisms at the level of differential calculus 4) The way the maps $\{T^V_k \}$ from Remark 3.1 look in differential geometry. |
| title | Some Constructions on Quantum Principal Bundles |
| topic | Quantum Algebra 46L87, 58B99 |
| url | https://arxiv.org/abs/2502.19702 |