Timeline for Trivial algebras given by generators and relations
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2016 at 15:47 | comment | added | BWW | Although this is undecidable there is the Knuth-Bendix aka noncommutative Groebner basis algorithm. This is implemented in magna, in the GAP package GBNP in Bergman and possibly in other places. If one of these terminates you are in luck, if not, you can't conclude anything. | |
| Mar 20, 2016 at 22:35 | comment | added | hänsel | @ycor: no, I mean there exist concrete single examples with very few relators and very few, simple and short Relations which are unknown whether they present the trivial Group. | |
| Mar 20, 2016 at 22:28 | comment | added | YCor | @hänsel I'm confused by your last statement. Do you mean that it is not known whether the triviality problem is decidable for group presentations with say, 2 generators and 3 relators? (btw this gives no bound on the degree of the corresponding polynomials in the group algebra) or do you refer to specific examples of presentations (then, this has little to do with the undecidability issue) | |
| Mar 20, 2016 at 20:43 | comment | added | hänsel | Unfortunately no. But I heard about examples in the Group case with only 2 or 3 relators and only 1 or 2 Relations which are up to now not known if they are trivial. Don't expect a solution in your case. Even in the smallest examples practically undecideable. | |
| Mar 20, 2016 at 20:38 | comment | added | Ehud Meir | Thanks for the answer. Do you know if there are some results if the dimension of $V$ and the degree of the $f_i$ polynomials are restricted? In my case $V$ is of dimension 3, and there are 5 polynomials, of degree 2 (that is- containing monomials of degree at most 2) | |
| Mar 20, 2016 at 20:37 | vote | accept | Ehud Meir | ||
| Mar 20, 2016 at 18:23 | review | First posts | |||
| Mar 20, 2016 at 18:33 | |||||
| Mar 20, 2016 at 18:18 | history | answered | hänsel | CC BY-SA 3.0 |