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p-adic dimensions in symmetric tensor categories in characteristic p

Author(s)
Etingof, Pavel I; Harman, Nate; Ostrik, Victor
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Abstract
To every object X of a symmetric tensor category over a field of characteristic p > 0 we attach p-adic integers Dim+(X) and Dim−(X) whose reduction modulo p is the categorical dimension dim(X) of X, coinciding with the usual dimension when X is a vector space. We study properties of Dim±(X), and in particular show that they don’t always coincide with each other, and can take any value in Z [subscript]p. We also discuss the connection of p-adic dimensions with the theory of λ-rings and Brauer characters. ©2018 Keywords: tensor categories; symmetric monoidal categories
Date issued
2018-02
URI
https://hdl.handle.net/1721.1/124324
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Quantum topology
Publisher
European Mathematical Publishing House
Citation
Etingof, Pavel, Nate Harman, and Victor Ostrik, "p-adic dimensions in symmetric tensor categories in characteristic p." Quantum topology 9, 1 (Feb. 2018): p. 119-40 doi:: 10.4171/QT/104 ©2018 Author(s)
Version: Author's final manuscript
ISSN
1664-073X
1663-487X

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