Comments on: Geometry of the Okubo algebra http://www.neverendingbooks.org/index.php/geometry-of-the-okubo-algebra.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 By: cyrus http://www.neverendingbooks.org/index.php/geometry-of-the-okubo-algebra.html/comment-page-1#comment-15576 cyrus Tue, 22 Feb 2011 12:05:44 +0000 http://www.neverendingbooks.org/?p=1407#comment-15576 i do have a theory called quantum superspinorial topology .... 4-d spacetime is 8-d spacetime -- forming a 4-complex manifold. good enough? i do have a theory called quantum superspinorial topology …. 4-d spacetime is 8-d spacetime — forming a 4-complex manifold. good enough?

]]> By: Carl Brannen http://www.neverendingbooks.org/index.php/geometry-of-the-okubo-algebra.html/comment-page-1#comment-8031 Carl Brannen Fri, 24 Apr 2009 00:13:19 +0000 http://www.neverendingbooks.org/?p=1407#comment-8031 <p>Is anyone here familiar with the subset of 3x3 matrices that are "magic", that is, where the sum of the three elements in a row or column does not depend on the row or column? These matrices are closed under addition and multiplication, include 0 and 1, and form a subgroup of the unitary matrices. They are related to the discrete Fourier transform on 3 vectors and 3 matrices, and on the permutation group on 3 elements. And they seem to have applications to the elementary particles.</p> <p>The unitary magic matrices form a manifold with 4 real dimensions. I've linked in an elegant parameterization that is 4-dimensional and appears, by computer calculation, to parameterize the whole group but I can't figure out how to prove it.</p> Is anyone here familiar with the subset of 3×3 matrices that are “magic”, that is, where the sum of the three elements in a row or column does not depend on the row or column? These matrices are closed under addition and multiplication, include 0 and 1, and form a subgroup of the unitary matrices. They are related to the discrete Fourier transform on 3 vectors and 3 matrices, and on the permutation group on 3 elements. And they seem to have applications to the elementary particles.

The unitary magic matrices form a manifold with 4 real dimensions. I’ve linked in an elegant parameterization that is 4-dimensional and appears, by computer calculation, to parameterize the whole group but I can’t figure out how to prove it.

]]> By: Mélanie http://www.neverendingbooks.org/index.php/geometry-of-the-okubo-algebra.html/comment-page-1#comment-7311 Mélanie Sun, 15 Mar 2009 20:41:34 +0000 http://www.neverendingbooks.org/?p=1407#comment-7311 <p>Thank you for this interesting and illuminating post (and for your kind words concerning my talk :-).</p> Thank you for this interesting and illuminating post (and for your kind words concerning my talk :-) .

]]> By: Daniel de França MTd2 http://www.neverendingbooks.org/index.php/geometry-of-the-okubo-algebra.html/comment-page-1#comment-7295 Daniel de França MTd2 Sun, 15 Mar 2009 04:33:16 +0000 http://www.neverendingbooks.org/?p=1407#comment-7295 <p>This looks like Twistors. Is this Algebra related to them?</p> This looks like Twistors. Is this Algebra related to them?

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