Timeline for Why were matrix determinants once such a big deal?
Current License: CC BY-SA 3.0
8 events
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| Jun 5, 2017 at 20:16 | comment | added | KConrad | @LSpice yes, but when I wrote my previous comment I didn't want to go back that far. The formula for discriminants of Galois extensions suggested to Dedekind the group determinant (ignore the square from discriminants). | |
| Jun 5, 2017 at 18:06 | comment | added | LSpice | @KConrad, a lot of my understanding of the history comes from your Enseign. Math. paper, so I don't want to correct, but didn't Dedekind's interest come from computing discriminants of field extensions, which are squares of specialisations of the group determinant? | |
| Jan 14, 2017 at 9:35 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
added doi and links
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| Feb 23, 2011 at 22:48 | comment | added | Greg Marks | Also, pleasantly (in contrast with the identical character tables of nonisomorphic extraspecial $p$-groups of the same order), nonisomorphic groups have different group determinants in characteristic $0$. See E. Formanek, D. Silbey, "The group determinant determines the group," Proc. Amer. Math. Soc. 112 (1991), no. 3, 649-656. | |
| Dec 23, 2010 at 1:39 | comment | added | KConrad | Guntram: Dedekind raised the question because in the case of abelian groups the answer was quite simple, in terms of characters of the group (homs from the group to the unit circle). So it's natural to ask what happens for nonabelian groups. He checked at least two examples (the groups S_3 and Q_8) and found certain patterns suggesting hypercomplex numbers might be relevant. For more details, read the paper by Hawkins which Stanley mentions in his answer. | |
| Dec 22, 2010 at 8:39 | comment | added | Guntram | So why did Dedekind raise this question? | |
| Aug 19, 2010 at 2:22 | comment | added | Tom Church | If anyone is interested in exploring Frobenius' results themselves, a nice version is written down as Exercise 3.33 of Fulton-Harris, "Representation Theory". | |
| Aug 19, 2010 at 1:46 | history | answered | Richard Stanley | CC BY-SA 2.5 |