Timeline for Making use of extra symmetries; more examples?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2021 at 14:21 | vote | accept | Student | ||
| Jan 15, 2021 at 22:29 | answer | added | Qiaochu Yuan | timeline score: 3 | |
| Jan 15, 2021 at 20:43 | comment | added | Benjamin Steinberg | If course if the group algebra were not semisimple you would not have an isotypic decomposition. But if you had some semisimple ring of R-endomorphisms you could use the isotypic decomposition from that one. | |
| Jan 15, 2021 at 20:41 | comment | added | Benjamin Steinberg | The fact that the isotypic components are preserved doesn't really need the projection. One way to define the isotypic component of a simple module S is as the sum of all submodules isomorphic to S. By Schur's lemma the image of a copy of S under an endomorphism is either 0 or another copy of S. So endomorphisms preserve isotypic components. Since R acts by endomorphisms of M wrt the G action it preserves the G-isotypic component | |
| Jan 15, 2021 at 20:39 | history | edited | Student | CC BY-SA 4.0 |
added 131 characters in body
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| Jan 15, 2021 at 20:25 | history | asked | Student | CC BY-SA 4.0 |