A geometric construction of the exceptional Lie algebras F4 and E8
Jos\'e Figueroa-O'Farrill
TL;DR
This paper introduces a geometric method to construct the exceptional Lie algebras F4 and E8 using spheres, inspired by supergravity algebra constructions, providing new insights into their geometric origins.
Contribution
It presents a novel geometric construction of F4 and E8 Lie algebras starting from spheres, distinct from previous algebraic approaches.
Findings
Constructs F4 and E8 from 8- and 15-spheres
Provides a geometric perspective on exceptional Lie algebras
Inspired by supergravity algebra structures
Abstract
We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)
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