Is the G-extension of a fusion category unique? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T16:34:34Z http://mathoverflow.net/feeds/question/113784 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113784/is-the-g-extension-of-a-fusion-category-unique Is the G-extension of a fusion category unique? Lucy Zhang 2012-11-19T00:33:23Z 2012-11-21T23:14:12Z <p>The definition reads that "A G-extension of a fusion category D is a G-graded fusion category C whose trivial component is equivalent to D." It seems like a priori there can be multiple G-extensions for the same fusion category D. Is that really the case (i.e. no reduction mechanism)? But there seems to be a "canonical one" at least, which has the same category D sitting on top of each component of the grading. Does this particular G-extension have a name?</p> http://mathoverflow.net/questions/113784/is-the-g-extension-of-a-fusion-category-unique/114115#114115 Answer by César Galindo for Is the G-extension of a fusion category unique? César Galindo 2012-11-21T23:14:12Z 2012-11-21T23:14:12Z <p>A complete reference for G-extension of fusion categories is <a href="http://arxiv.org/abs/0909.3140" rel="nofollow">http://arxiv.org/abs/0909.3140</a> (see also <a href="http://arxiv.org/abs/0911.0881" rel="nofollow">http://arxiv.org/abs/0911.0881</a>). The kind of examples that you are saying are $\mathcal D\boxtimes \text{Vec}_G$, the Deligne product of $\mathcal D$ with Vec$_G$.</p>