Structures · Data types
Bracket
The Bracket class has three intended uses:
1. for certain binary operations on structures, like the product ⁅x, y⁆ of two elements
x, y in a Lie algebra or the commutator of two elements x and y in a group.
2. for certain actions of one structure on another, like the action ⁅x, m⁆ of an element x
of a Lie algebra on an element m in one of its modules (analogous to SMul in the
associative setting).
3. for binary operations on substructures, like the commutator ⁅H, K⁆ of two subgroups H and
K of a group.
- Defined in
- Mathlib.Data.Bracket
- Shape
- 2 explicit arguments · adds bracket
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by3
Forgetful instances
Provided automatically by
Concrete types that are instances12
- TensorProduct
- AddSubgroup
- LieIdeal
- Derivation
- LieDerivation
- LeftInvariantDerivation
- LieAlgebra.SemiDirectSum
- AddGroupLieAlgebra
- GroupLieAlgebra
- Subtype
- HasQuotient.Quotient
- Subgroup
How is a type an instance?
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Assumed by7
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No ancestors.