- journal article metadata
European Mathematical Society Publishing House
2018-02-04 23:30:02
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2018
1
$p$-adic dimensions in symmetric tensor categories in characteristic $p$
Pavel
Etingof
Massachusetts Institute of Technology, Cambridge, USA
Nate
Harman
University of Chicago, USA
Victor
Ostrik
University of Oregon, Eugene, USA
Tensor categories, symmetric monoidal categories
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$_{\pm}(X)$, and in particular show that they don't always coincide with each other, and can take any value in $\mathbb Z_p$. We also discuss the connection of $p$-adic dimensions with the theory of $\lambda$-rings and Brauer characters.
Category theory; homological algebra
119
140
10.4171/QT/104
http://www.ems-ph.org/doi/10.4171/QT/104
2
1
2018