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