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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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