Short Introduction to Planar Algebras - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T01:05:31Z http://mathoverflow.net/feeds/question/873 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/873/short-introduction-to-planar-algebras Short Introduction to Planar Algebras Elisha Peterson 2009-10-17T13:40:09Z 2009-11-17T06:17:58Z <p>Are there any good <strong>short</strong> expositions of planar algebras out there? I am interested primarily in seeing the main definition and some explicit examples.</p> http://mathoverflow.net/questions/873/short-introduction-to-planar-algebras/874#874 Answer by Scott Morrison for Short Introduction to Planar Algebras Scott Morrison 2009-10-17T14:05:43Z 2009-10-17T14:05:43Z <p>My paper with Emily and Noah about the <a href="http://arxiv.org/abs/0808.0764" rel="nofollow"><code>D_{2n}</code> planar algebra</a> includes our attempt at a friendly explanation. It's all about arguably the simplest non-trivial example of a <em>subfactor</em> planar algebra.</p> http://mathoverflow.net/questions/873/short-introduction-to-planar-algebras/880#880 Answer by David Speyer for Short Introduction to Planar Algebras David Speyer 2009-10-17T14:30:08Z 2009-10-18T04:38:33Z <p>Emily and Noah wrote some really nice expository posts on planar algebras at the <a href="http://sbseminar.wordpress.com/category/planar-algebras/" rel="nofollow">Secret Blogging Seminar</a>. I also like Chris's posts on TQFTs and Planar Algebras to explain why I might care. </p> http://mathoverflow.net/questions/873/short-introduction-to-planar-algebras/2476#2476 Answer by Emily Peters for Short Introduction to Planar Algebras Emily Peters 2009-10-25T14:51:11Z 2009-10-25T14:51:11Z <p>Vaughan Jones' paper "<a href="http://math.berkeley.edu/~vfr/delphi.ps" rel="nofollow">The planar algebra of a bipartite graph</a>" is short and example-focused. It's got the "right" definition (phrased with operads) and the mechanics of the bipartite graph planar algebra. While the bipartite graph planar algebra isn't a subfactor planar algebra, it's pretty darn close. </p> <p>A subfactor planar algebra, by the way, is one which meets restrictions on the sizes of the spaces involved and has an inner product. Unsurprisingly, they give rise to subfactors (through machinery of Popa).</p>