Timeline for What's "geometric algebra"?
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2021 at 11:18 | answer | added | Siddharth Bhat | timeline score: 5 | |
| Nov 25, 2021 at 1:08 | answer | added | paul garrett | timeline score: 5 | |
| Nov 24, 2021 at 19:06 | comment | added | wlad | I include all possible geometric interpretations. Maybe therefore Geometric Algebras are Clifford algebras equipped with additional structure. Different structures on the same CA give rise to different GAs. | |
| Nov 24, 2021 at 17:36 | comment | added | wlad | In my answer, I suggest it's a name for an arbitrary Clifford algebra + a geometric interpretation of it. I don't know whether this can be captured formally in a way that covers the full breadth of what gets called "geometric algebra". It's a bit like how a group can be equipped with an action which makes it more than just an abstract group. | |
| Nov 24, 2021 at 17:00 | answer | added | wlad | timeline score: 5 | |
| Aug 14, 2020 at 21:50 | answer | added | David Jones | timeline score: 11 | |
| Jun 11, 2020 at 23:56 | answer | added | amathematician | timeline score: 7 | |
| Mar 14, 2020 at 10:48 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Feb 18, 2020 at 13:24 | answer | added | AlexArvanitakis | timeline score: 4 | |
| Feb 11, 2020 at 19:18 | comment | added | Gotthold | I'd just like to add that ncatlab has a brief page on this issue: ncatlab.org/nlab/show/geometric+algebra. Essentially it is an issue of presentation, trying to avoid both explicit representation by matrices and also quotients of tensor algebras, though I should also note that Hestenes in his public comments has been very adamant that somehow this distinction is very important in terms of new applications (see physicsforums.com/insights/…). | |
| Feb 10, 2020 at 21:17 | comment | added | arsmath | I have been wondering this question a lot lately, so I'm glad you asked it. I know the theory of Clifford algebras, and I don't understand the miraculous qualities attributed to them. | |
| Feb 10, 2020 at 18:07 | comment | added | Qfwfq | @GP Typo: I meant to write "wasn't aware of the book, thank you" | |
| Feb 10, 2020 at 16:28 | comment | added | AlexArvanitakis | It is essentially the same as Clifford algebras, quaternions, etc. equipped with non-standard notation. Usually the context for this is indeed applications to physics where it is argued that their notation is nicer | |
| Feb 10, 2020 at 15:58 | comment | added | Qfwfq | @GP: no, I was aware of that book, thank you. But I think probably the "GA" in my OP isn't related to axiomatic projective geometries. | |
| Feb 10, 2020 at 15:48 | comment | added | Gerhard Paseman | Are you aware of Emil Artin's book of that title? It mostly has to do with the axiomatic investigation of projective geometries and (among other things) their coordinatization derived from the postulated symmetries. It's possible that what you are asking is inspired or developed from this text, but I don't know enough to give a proper answer. Gerhard "Starting A Change..." Paseman, 2020.02.10. | |
| Feb 10, 2020 at 15:31 | history | edited | YCor |
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| Feb 10, 2020 at 15:15 | history | edited | Qfwfq | CC BY-SA 4.0 |
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| Feb 10, 2020 at 15:08 | history | asked | Qfwfq | CC BY-SA 4.0 |