Timeline for Subalgebras of matrices
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 5, 2022 at 11:00 | history | edited | coudy | CC BY-SA 4.0 |
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| Jun 10, 2010 at 7:55 | comment | added | coudy | @chana. Burnside theorem shows that a proper subalgebra of M_2(C) is reducible. That means that there is a non-zero vector in $C^2$ which is an eigenvector for all matrices in the subalgebra. Using that vector as the first element of a new basis, you can check that, in that new basis, all elements of the subalgebra are upper triangular matrices. Then it is not very difficult to list all the subalgebras of 2x2 upper triangular matrices (First case: all elements are diagonal matrices. Second case: there is an element which is not diagonal). | |
| Jun 9, 2010 at 15:34 | comment | added | chana | I am not sure I know why Burnside theorem implies the list of subalgebras of M_2(C) you suggested. (I am interested in subalgebras with 1, so your list is ok to me). Also, what if instead of $C$ you take $k(X)$ where $k$ is any field? | |
| Jun 7, 2010 at 19:05 | history | answered | coudy | CC BY-SA 2.5 |