Timeline for Algebraic relation given by a 3x3 determinant
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 28, 2020 at 5:02 | comment | added | Per Alexandersson | I was told that this looks a lot like the Yang-Baxter relation. This seem to fit the broader picture I am looking at. | |
| Apr 10, 2020 at 6:51 | comment | added | Per Alexandersson | @MarkSapir: No, that is not my question - I consider this as part of the relations which hold. For example, whenever you see the relation $aba=bab$, you might think 'Braid relation!'. I wonder if the determinant relation above gives a similar reaction. | |
| Apr 9, 2020 at 22:39 | comment | added | Libli | @PerAlexandersson : I have the feeling it would be easier if you would explain the concrete example you are working with in more details. | |
| Apr 9, 2020 at 21:59 | history | edited | Zach Teitler | CC BY-SA 4.0 |
typo in formula
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| Apr 9, 2020 at 21:41 | comment | added | YCor | But your determinant has plenty of non-equivalent ways to be read, unless you specify precisely rules. Formally: you want to choose a lift from the determinant formula from the polynomial algebra in $n^2$ variables to the non-commutative one. Probably you implicitly have such a lift in your mind. | |
| Apr 9, 2020 at 21:34 | comment | added | Per Alexandersson | @MarkWildon I realized that the question was poorly worded, and I hope it is now clarified. Basically, I have a relation given by a 'determinant' where multiplication is non-commutative, and wonder if this type of non-commutative relation has any meaning. | |
| Apr 9, 2020 at 21:33 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
clarified
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| Apr 9, 2020 at 13:42 | comment | added | Mark Wildon | I don't understand the question at all. The free non-commutative algebra on $\{a,b,c,x,y,z\}$ has as a basis all ordered monomials in the letters. So $bz$ is linearly independent of $cz, ay, az, bx, cy$, ruling out the relation you claim holds. What algebra are we working in? Is your question really: `if this relation holds, what can deduce about related determinants?' | |
| Apr 9, 2020 at 12:52 | comment | added | Per Alexandersson | The formula stated below the determinant. That is, "Sarrus' rule". I am mainly interested in the 3x3 case (as that's what I encountered). | |
| Apr 9, 2020 at 12:05 | comment | added | abx | What is your definition of the determinant in a non-commutative algebra? | |
| Apr 9, 2020 at 11:46 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
added 14 characters in body
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| Apr 9, 2020 at 11:21 | history | asked | Per Alexandersson | CC BY-SA 4.0 |