Isocategorical groups
| dc.creator | Etingof, Pavel | |
| dc.creator | Gelaki, Shlomo | |
| dc.date | 2000-07-31 | |
| dc.date.accessioned | 2026-07-25T22:50:53Z | |
| dc.description | It is well known that if two finite groups have the same symmetric tensor categories of representations over C, then they are isomorphic. We study the following question: when do two finite groups G1,G2 have the same tensor categories of representations over C (without regard for the commutativity constraint). We call two groups with such property isocategorical. We give an example of two groups which are isocategorical but not isomorphic: the affine symplectic group of a vector space over the field of two elements, and an appropriate "affine pseudosymplectic group" introduced by R.Griess (containing the "pseudosymplectic group" of A.Weil). On the other hand, we give a classification of groups isocategorical to a given group. In particular, we show that if G has no nontrivial normal subgroups of order 2^{2m} then any group isocategorical to G must actually be isomorphic to G. The proofs use the theory of triangular Hopf algebras. We also apply the notion of isocategorical groups to studying the question: when are two triangular semisimple Hopf algebras isomorphic as Hopf algebras? | |
| dc.description | 17 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0007196 | |
| dc.identifier | http://arxiv.org/abs/math/0007196 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/93076 | |
| dc.subject | Quantum Algebra | |
| dc.title | Isocategorical groups | |
| dc.type | text |