p-adic dimensions in symmetric tensor categories in characteristic p
Name
1510.04339.pdf
Description
Accepted version
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230.29 KB
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Author(s)
Etingof, Pavel I
Harman, Nate
Ostrik, Victor
Date Issued
February 2018
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
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4171/QT/104
