User katie - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:58:09Z http://mathoverflow.net/feeds/user/6985 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118868/distributive-sublattices-of-atomistic-ortholattices distributive sublattices of atomistic ortholattices Katie 2013-01-14T11:07:23Z 2013-01-14T13:58:10Z <p>Let $L$ be an atomistic ortholattice (i.e. every element can be written as a join of atoms) with top and bottom elements 0 and 1, and let $M$ be a distributive atomic sub-ortholattice of $L$.</p> <p>Is $M$ generated by its atoms, in the sense that every element in $M$ can be written as a join of the atoms in $M$?</p> http://mathoverflow.net/questions/32511/homomorphisms-between-matrix-algebras *-homomorphisms between matrix algebras Katie 2010-07-19T16:35:00Z 2013-01-13T21:17:43Z <p>Edited question:</p> <p>Are there any other non-trivial *-homomorphisms between matrix algebras apart from the unitary homomorphisms? </p> <p>Original question:</p> <p>Does there exist a surjective (but not bijective) *-homomorphism between matrix algebras over the complex numbers? If so, are there any nice examples?</p> <p>(I had not realized the matrix algebras were simple but since they are, the answer to the original question is indeed obvious)</p> http://mathoverflow.net/questions/29087/commutative-subalgebras-of-m-n Commutative subalgebras of M_n Katie 2010-06-22T13:36:52Z 2010-08-03T18:55:30Z <p>For a given $n$, is there any characterization for the commutative subalgebras of $M_n(\Bbb{C})$? I would like to know how many commutative subalgebras there are for each possible dimension.</p> <p>In view of Chapman's answer, I am refining my previous question:</p> <p>Given $k\leq n$, is there any way of describing the commutative subalgebras of $M_n$ which are of dimension $k$.</p> http://mathoverflow.net/questions/118868/distributive-sublattices-of-atomistic-ortholattices/118869#118869 Comment by Katie Katie 2013-01-15T15:16:17Z 2013-01-15T15:16:17Z Thanks guys, this was helpful. http://mathoverflow.net/questions/118868/distributive-sublattices-of-atomistic-ortholattices/118869#118869 Comment by Katie Katie 2013-01-14T14:02:19Z 2013-01-14T14:02:19Z as a side question, I've added a comment in the edit summary box, but the comment doesn't seem to appear anywhere now, am I missing something? http://mathoverflow.net/questions/118868/distributive-sublattices-of-atomistic-ortholattices/118869#118869 Comment by Katie Katie 2013-01-14T13:56:55Z 2013-01-14T13:56:55Z Yes, good idea about the comment. I understand atomic to mean that $M$ has atoms, while atomistic means that every element is a join of atoms. http://mathoverflow.net/questions/118868/distributive-sublattices-of-atomistic-ortholattices/118869#118869 Comment by Katie Katie 2013-01-14T13:07:08Z 2013-01-14T13:07:08Z what if I impose the additional condition that $M$ is atomic? http://mathoverflow.net/questions/29087/commutative-subalgebras-of-m-n/30849#30849 Comment by Katie Katie 2010-07-07T11:04:29Z 2010-07-07T11:04:29Z I actually needed a characterisation of self-adjoint commutative algebras, but I didn't realize it until I saw this answer. Thanks