Symmetric tensor categories in characteristic 2

2018/07/15 by Benson, Dave, Etingof, Pavel · 4 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1807.05549

Abstract

We construct and study a nested sequence of finite symmetric tensor categories \rm Vec=C₀⊂ C₁⊂⋯⊂ C_n⊂⋯ over a field of characteristic 2 such that C_2n are incompressible, i.e., do not admit tensor functors into tensor categories of smaller Frobenius--Perron dimension. This generalizes the category C₁ described by Venkatesh and the category C₂ defined by Ostrik. The Grothendieck rings of the categories C_2n and C_2n+1 are both isomorphic to the ring of real cyclotomic integers defined by a primitive 2ⁿ⁺²-th root of unity, O_n=\mathbb Z[2cos(π/2ⁿ⁺¹)].

Cited by

• A special class of prime ideals for infinite symmetric group algebras
• A conjecture on the tensor ideal for an elementary p-group generated by the restriction of a Steinberg module
• Group schemes and their Lie algebras over a symmetric tensor category
• Homogeneous spaces in tensor categories

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