A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Ocal, Pablo S. Ueyama, Kenta Veerapen, Padmini |
| author_facet | Ocal, Pablo S. Ueyama, Kenta Veerapen, Padmini |
| contents | We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the classification and properties of twisted tensor products, and we examine twisted Segre products. Our exposition emphasizes clarity over generality, providing a wealth of interconnecting examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15885 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry Ocal, Pablo S. Ueyama, Kenta Veerapen, Padmini Rings and Algebras Quantum Algebra Representation Theory 16S80 (Primary) 16S38, 16T99, 14A22 (Secondary) We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the classification and properties of twisted tensor products, and we examine twisted Segre products. Our exposition emphasizes clarity over generality, providing a wealth of interconnecting examples. |
| title | A Primer on Twists in the Noncommutative Realm Focusing on Algebra, Representation Theory, and Geometry |
| topic | Rings and Algebras Quantum Algebra Representation Theory 16S80 (Primary) 16S38, 16T99, 14A22 (Secondary) |
| url | https://arxiv.org/abs/2211.15885 |