The algebraic closure for the Ree family of type G₂ #
This file records that the algebraic closure attached to a validated Ree index of type G₂ has
characteristic three, and equips it with the resulting structure of an algebra over the field of
three elements. This is the base ring over which the family's short-root carrier is defined.
Main results #
TauCeti.ReeG2LieIndex.charP_closure_three: the algebraic closure attached to a Ree index of typeG₂has characteristic three.TauCeti.ReeG2LieIndex.algebraZModThree: the resultingZMod 3-algebra structure on it.
The algebraic closure attached to a Ree index of type G₂ has characteristic three.
@[instance_reducible]
The algebraic closure attached to a Ree index of type G₂ is an algebra over the field of
three elements, the base ring of the family's carrier. Characteristic three determines this
structure uniquely.
Equations
- d.algebraZModThree = ZMod.algebra (↑d).Closure 3