2024-12-03 15:08:14 +00:00
|
|
|
/-
|
|
|
|
|
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
|
|
|
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
|
|
|
Authors: Joseph Tooby-Smith
|
|
|
|
|
-/
|
|
|
|
|
import Mathlib.RingTheory.GradedAlgebra.Basic
|
2024-12-05 06:49:50 +00:00
|
|
|
import HepLean.Meta.Informal.Basic
|
2024-12-03 15:08:14 +00:00
|
|
|
/-!
|
|
|
|
|
|
|
|
|
|
# Super Algebras
|
|
|
|
|
|
|
|
|
|
A super algebra is a special type of graded algebra.
|
|
|
|
|
|
|
|
|
|
It is used in physics to model the commutator of fermionic operators among themselves,
|
|
|
|
|
aswell as among bosonic operators.
|
|
|
|
|
|
|
|
|
|
-/
|
|
|
|
|
|
|
|
|
|
informal_definition SuperAlgebra where
|
|
|
|
|
math :≈ "A super algebra is a graded algebra A with a ℤ₂ grading."
|
|
|
|
|
physics :≈ "A super algebra is used to model the commutator of fermionic operators among
|
|
|
|
|
themselves, aswell as among bosonic operators."
|
|
|
|
|
ref :≈ "https://en.wikipedia.org/wiki/Superalgebra"
|
2024-12-03 15:26:06 +00:00
|
|
|
|
|
|
|
|
namespace SuperAlgebra
|
|
|
|
|
|
|
|
|
|
informal_definition superCommuator where
|
|
|
|
|
math :≈ "The commutator which for `a ∈ Aᵢ` and `b ∈ Aⱼ` is defined as `ab - (-1)^(i * j) ba`."
|
|
|
|
|
deps :≈ [``SuperAlgebra]
|
|
|
|
|
|
|
|
|
|
end SuperAlgebra
|
