Timeline for Subalgebras of matrices
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2010 at 0:07 | comment | added | Victor Protsak | I am referring to "wild representation type": classification of its modules contains as a subproblem classifying all pairs of matrices up to conjugation. By Drozd's theorem, a finite-dimensional algebra $A$ is either of finite, tame, or wild type. There are parameters in isomorphism classes of $A$-modules $\implies$ $A$ is not finite or tame $\implies$ $A$ is wild. | |
| Jun 8, 2010 at 20:34 | comment | added | Mariano Suárez-Álvarez | Heh. Of course there will be module as in (a)! I was just observing that the OP's question was slightly different than the one you answered. What do you mean by "moduli of individual wild algebras"? | |
| Jun 8, 2010 at 15:34 | comment | added | Victor Protsak | Yes, you can do it for a few small values of $n$, but there will be (a) moduli of associative algebras of a given dimension $k$; and (b) moduli of individual wild algebras present even for a fixed $n$ once it is large enough. | |
| Jun 8, 2010 at 12:10 | comment | added | Mariano Suárez-Álvarez | The question is asking for the subalgebas of one matrix algebra, as far as I can tell, which is a different problem than classifying all f.d. algebras with a faithful representation (ie, all algebras) | |
| Jun 8, 2010 at 0:18 | history | answered | Victor Protsak | CC BY-SA 2.5 |