JournalsqtVol. 9, No. 1pp. 119–140

pp-adic dimensions in symmetric tensor categories in characteristic pp

  • Pavel Etingof

    Massachusetts Institute of Technology, Cambridge, USA
  • Nate Harman

    University of Chicago, USA
  • Victor Ostrik

    University of Oregon, Eugene, USA
$p$-adic dimensions in symmetric tensor categories in characteristic $p$ cover

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Abstract

To every object XX of a symmetric tensor category over a field of characteristic p>0p>0 we attach pp-adic integers Dim+(X)_+(X) and Dim(X)_-(X) whose reduction modulo pp is the categorical dimension dim(X)(X) of XX, coinciding with the usual dimension when XX is a vector space. We study properties of Dim±(X)_{\pm}(X), and in particular show that they don't always coincide with each other, and can take any value in Zp\mathbb Z_p. We also discuss the connection of pp-adic dimensions with the theory of λ\lambda-rings and Brauer characters.

Cite this article

Pavel Etingof, Nate Harman, Victor Ostrik, pp-adic dimensions in symmetric tensor categories in characteristic pp. Quantum Topol. 9 (2018), no. 1, pp. 119–140

DOI 10.4171/QT/104