Timeline for Subalgebras of matrices
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2010 at 18:17 | comment | added | Bugs Bunny | And, off course, classifying them will require quotients and basically hopeless unless you restrict a certain class of algebras, like semisimple or with square of Jacobson rad zero or 3-nilpotent. | |
| Jun 9, 2010 at 18:15 | comment | added | Bugs Bunny | I disagree, Victor. The problem is "to describe" and not "to classify". If $V$ is a regular representations then choosing a generic element identifies $V$ with the algebra. Thus, it is exactly describing associative algebra structures on $V$. This can be described in a useful way by writing multiplication tensor!! | |
| Jun 9, 2010 at 6:29 | comment | added | Victor Protsak | Even projective is probably too much to ask for: the regular module of an $n$-dimensional algebra is an $n$-dimensional projective module. So in this case, an apparent subproblem is to classify all $n$-dimensional associative algebras. Good luck with that... | |
| Jun 7, 2010 at 23:46 | history | answered | Bugs Bunny | CC BY-SA 2.5 |