Timeline for Can you compute the quotient set below?
Current License: CC BY-SA 3.0
9 events
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| May 4, 2013 at 18:43 | comment | added | Gigel Militaru | Yes, I know the paper of de Graaf and is a very nice one. The niplotent condition, that is his interest, is a very strog one -- in dimension $2$ there are only $2$ niplotent algebras. Our classifying object $K \times K / \equiv$ can be an infinite set if $K \neq k^2$. It's a very strange problem: so elementary and so ... | |
| May 4, 2013 at 18:34 | comment | added | Dietrich Burde | @Gigel Militaru: you are right. I edited my answer accordingly. | |
| May 4, 2013 at 18:33 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
added 89 characters in body
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| May 4, 2013 at 18:10 | comment | added | Gigel Militaru | PS: Now I got it. By 'algebras' the authors do not assume associative and unitary algebras. They just take a biliniar map -- with no other axioms. However, they do not answer my question that remains open - in characteristic $2$ they work only over the field with two elements $Z_2$. Well, in this case everyone can discribe that quotient set. The big problem with it is the case $K \neq k^2$. | |
| May 4, 2013 at 17:54 | comment | added | Dietrich Burde | The 52 classes also include the non associative ones, I think. By algebra the authors mean any $K$-algebra. | |
| May 4, 2013 at 17:53 | comment | added | Harry Altman | Link nitpick: When linking to arXiv, please link to the abstract, not directly to the PDF. | |
| May 4, 2013 at 17:36 | comment | added | Gigel Militaru | Thank you very much for the link. Yes, I know the classification of Peirce etc --was done until now up to dimension 6. But this holds only for algebraically closed fields with characteristc $\neq 2$. For arbitrary fields, in particular in characteristic $2$, there are big troubles (that qoutient set above is responsible for it). The paper that you indicate is from 2012 and I have to contact the authors since over $Z_2$ is not posible to exists 52 classe of isomorphisms of algebras of dimension 2 as they claim on pag. 10. Too many :) | |
| May 4, 2013 at 17:15 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
edited body
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| May 4, 2013 at 16:27 | history | answered | Dietrich Burde | CC BY-SA 3.0 |