Isocategorical groups (Q2708376)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isocategorical groups |
scientific article |
Statements
14 August 2001
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tensor categories
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symplectic groups
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triangular Hopf algebras
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finite groups
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complex representations
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Isocategorical groups (English)
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Two finite groups \(G_1\), \(G_2\) are called isocategorical if the categories \(\text{Rep}(G_1)\), \(\text{Rep}(G_2)\) of their finite-dimensional complex representations are equivalent as tensor categories. The authors show that, in this case, \(G_1\) and \(G_2\) are two closely related extensions of a finite group \(K\) by an Abelian group \(A\) of order \(2^{2m}\), for some integer \(m\). A nontrivial example is given where \(G_1\) is the affine symplectic group of a vector space \(V=A\) over the field with 2 elements. The proofs use ideas from Hopf algebras.
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