Timeline for Classifying Hopf algebras that admit a single irreducible comodule
Current License: CC BY-SA 4.0
9 events
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| Aug 14, 2021 at 18:08 | history | edited | Konstantinos Kanakoglou | CC BY-SA 4.0 |
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| Aug 12, 2021 at 21:12 | vote | accept | Spyros Olympopolous | ||
| Aug 12, 2021 at 21:02 | comment | added | Konstantinos Kanakoglou | If we are speaking about HAs then the presence of $1$ makes the connected and the irreducibles the same thing. Since then the trivial (1-dim) comodule always makes sense. | |
| Aug 12, 2021 at 20:57 | comment | added | Konstantinos Kanakoglou | @Spyros, a connected coalgebra has a unique simple comodule, which must be 1-dim. An irreducible one has a unique simple comodule. So at the level of coalgebras, connected are irreducibles (but not necessarily the other way around). So the irreducibles are a wider class. | |
| Aug 12, 2021 at 20:33 | history | edited | Konstantinos Kanakoglou | CC BY-SA 4.0 |
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| Aug 12, 2021 at 18:12 | comment | added | Spyros Olympopolous | Thanks for your answer. Just so I understand precisely - irreducible is a special of connected? Precisely an irreducible Hopf algebras is one that has a single comodule, namely the trivial comodule, and hence it is connected since connected requires the weaker condition of the existence of a single 1-dim comodule. Is this correct. | |
| Aug 12, 2021 at 11:11 | history | edited | Konstantinos Kanakoglou | CC BY-SA 4.0 |
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| Aug 12, 2021 at 6:43 | vote | accept | Spyros Olympopolous | ||
| Aug 12, 2021 at 6:45 | |||||
| Aug 12, 2021 at 1:07 | history | answered | Konstantinos Kanakoglou | CC BY-SA 4.0 |