In this supercool paper, the authors define a tripled Fano plane (yes, that's right, three copies of Furey's particle zoo). It describes a set of $21 = 3 \times 7$ (left cyclic) modules over a noncommutative ring on eight elements. The ring is given by the upper triangular $2 \times 2$ matrices over the field with two elements. Similarly for right cyclic modules.
The authors are familiar with the connection between octonion physics and so called stringy black holes. They find it odd that this structure is not studied in physics.
6 years ago