Timeline for Canonical examples of algebraic structures
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2011 at 16:49 | comment | added | Ryan Reich | @darij: $S_n$ may be more basic, but $\operatorname{GL}_n$ is (to me) more transparent. I can see the structure: it contains $S_n$; it gives me examples of unipotent and solvable groups too; there's also a nice description (over $\mathbb{C}$) of the conjugacy classes. Also, of course, it reminds me of highest-weight theory for representations of reductive groups (even better than $\operatorname{SL}_n$, which is not fully reductive). I find the last one rather useful because of personal bias. Not as close to the axioms, maybe, but richer. | |
| Oct 27, 2011 at 15:44 | comment | added | darij grinberg | I can't believe somebody finds $\mathrm{GL}_n$ or dihedral groups more basic than $S_n$. | |
| Jun 20, 2011 at 19:41 | comment | added | Mariano Suárez-Álvarez | @Sean: $sl_2$ is deceptively simple... I would say that $sl_3$ is a more representative example. | |
| Nov 11, 2010 at 1:53 | comment | added | Sean Tilson | I especially like sl_2 for lie algebra. I remember being amazed at how the representation theory of $sl_2$ gives you a good model to go about classifying all finite dimensional simple lie algebra over $\mathbb{C}$ | |
| Jan 8, 2010 at 14:39 | history | edited | user1073 | CC BY-SA 2.5 |
added 11 characters in body
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| Nov 6, 2009 at 13:43 | vote | accept | John D. Cook | ||
| Oct 30, 2009 at 6:29 | history | answered | Myron Minn-Thu-Aye | CC BY-SA 2.5 |