Timeline for Polynomial identities for mod p matrices
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 15, 2013 at 6:56 | comment | added | Mariano Suárez-Álvarez | @AaronMeyerowitz, I actually did not write exactly what I meant: the theorem A-L prove is that a non-zero identity of minimal degree is homogeneous and equal (up to a scalar) to the standard one if either $n>2$ or the field has more than two elements (they show that there exist identitie of minimal degree which are not homogeneous in the two exceptional cases: in $M_1(\mathbb F_2)$ one can take $x^2-x$, for example) | |
| Jul 13, 2013 at 13:21 | comment | added | Idanps | I am sorry if I miss something trivial, being an outsider to this area: How can I use the Amitsur-Levitzky theorem to bound the "lower degree" of a non-homogeneous polynomial identity? | |
| Jul 13, 2013 at 11:57 | comment | added | Benjamin Steinberg | No for both at once by Mariano's comment. | |
| Jul 13, 2013 at 5:39 | comment | added | Idanps | Thank you for your answer, David. My question is however if there exists a polynomial satisfying both 1) and 2). | |
| Jul 12, 2013 at 23:12 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 48 characters in body
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| Jul 12, 2013 at 22:04 | comment | added | Benjamin Steinberg | The answer is CW so please edit and fix. | |
| Jul 12, 2013 at 20:45 | comment | added | Aaron Meyerowitz | This standard polynomial does not use the field. It holds for any $2n$ $n \times n$ matrices with symbolic entries. | |
| Jul 12, 2013 at 20:32 | history | made wiki | Post Made Community Wiki by Benjamin Steinberg | ||
| Jul 12, 2013 at 19:32 | comment | added | Mariano Suárez-Álvarez | The smallest degree of a homogeneous polynomial identity on $n\times n$ matrices is $2n$ if $n>2$ or $p$ is odd, according to Amitsur and Levitzky. | |
| Jul 12, 2013 at 18:56 | history | answered | Benjamin Steinberg | CC BY-SA 3.0 |