most recent 30 from http://mathoverflow.net 2013-05-23T08:36:56Z http://mathoverflow.net/feeds/question/19551 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19551/software-for-planar-algebras-or-group-rings John Mangual 2010-03-27T22:45:51Z 2010-03-28T07:16:20Z

<p>Does software exists for calculating with planar algebras or group rings? It could be part of Mathematica or be an extension of Python or Java or C. What would go into designing such a data-type anyway? One would have to define a special class describing elements of your algebra and overload "+" and "x" so it felt natural. </p> <p>This request comes about because I am too lazy to write out all 16 terms in the <a href="http://en.wikipedia.org/wiki/Young_symmetrizer" rel="nofollow">young symmetrizer</a> for the partition (2,2) and show that representation is two-dimensional space. This will be even more unwieldy for larger partitions.</p> <p>It would also be difficult to do computations with the Templerley-Lieb algebras without software.</p> <p>An alternative question is: are there efficient ways to compute with Specht modules or the Temperley-Lieb algebras by hand?</p>

http://mathoverflow.net/questions/19551/software-for-planar-algebras-or-group-rings/19560#19560 John Palmieri 2010-03-27T23:58:23Z 2010-03-27T23:58:23Z

<p><a href="http://www.sagemath.org" rel="nofollow">Sage</a> can do some things with group algebras, in particular, with group algebras for symmetric groups, but it doesn't seem to have anything about planar algebras. For example:</p> <pre><code>S = SymmetricGroupAlgebra(ZZ, 3) # ZZ, the integers, is the coefficient ring # "3" means the symmetric group on 3 letters a = S([2,1,3]) # turn the permutation [2,1,3] into an element of S b = S([3,1,2]) (2*a + b)^2 </code></pre> <p>prints out</p> <pre><code>4*[1, 2, 3] + 2*[1, 3, 2] + [2, 3, 1] + 2*[3, 2, 1] </code></pre> <p>If you'd started with a different coefficient ring:</p> <pre><code>S = SymmetricGroupAlgebra(GF(3), 3) </code></pre> <p>then the output from the above would be</p> <pre><code>[1, 2, 3] + 2*[1, 3, 2] + [2, 3, 1] + 2*[3, 2, 1] </code></pre> <p>You can also do computations with other group algebras for other groups, but symmetric group algebras seem to be a bit better developed.</p>

http://mathoverflow.net/questions/19551/software-for-planar-algebras-or-group-rings/19595#19595 Mikael Vejdemo-Johansson 2010-03-28T06:53:18Z 2010-03-28T06:53:18Z

<p>Both Magma and GAP contain interfaces for doing computations with group algebras.</p>

http://mathoverflow.net/questions/19551/software-for-planar-algebras-or-group-rings/19597#19597 Bruce Westbury 2010-03-28T07:16:20Z 2010-03-28T07:16:20Z

<p>If there is software for planar algebras I would interested in hearing about it.</p> <p>For working in the Hecke algebra see my answer to <a href="http://mathoverflow.net/questions/19589/do-jones-wenzl-idempotents-lift-to-anything-interesting-in-the-hecke-algebra" rel="nofollow">http://mathoverflow.net/questions/19589/do-jones-wenzl-idempotents-lift-to-anything-interesting-in-the-hecke-algebra</a> and for the one specific question you ask see my answer to Sammy's previous question <a href="http://mathoverflow.net/questions/3299/does-the-super-temperley-lieb-algebra-have-a-z-form/19106#19106" rel="nofollow">http://mathoverflow.net/questions/3299/does-the-super-temperley-lieb-algebra-have-a-z-form/19106#19106</a></p> <p>You should be able to do what you want by hand. If you can't then can you say what the problem is.</p> <p>Also I don't see the connection between the two problems. How would planar algebra software help you with these algebras?</p>