Gradings on the Albert Algebra and on $f_4$
Cristina Draper, C\'andido Mart\'in
TL;DR
This paper classifies and analyzes the structure of group gradings on the Albert algebra and the exceptional Lie algebra _4 over algebraically closed fields of characteristic zero, identifying all nonequivalent gradings.
Contribution
It provides a complete classification of nontoral nonequivalent gradings on both the Albert algebra and _4, including the identification of fine gradings.
Findings
Eight nontoral nonequivalent gradings on the Albert algebra
Nine nontoral nonequivalent gradings on _4
Three fine gradings on each algebra
Abstract
We study group gradings on the Albert algebra and on the simple exceptional Lie algebra over algebraically closed fields of characteristic zero. There are eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on (also three of them fine).
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry