Struct HopfAlgebra 

pub struct HopfAlgebra {
    pub name: String,
    pub is_cocommutative: bool,
    pub antipode_involutive: bool,
}

A Hopf algebra: a bialgebra with an antipode map.

A Hopf algebra (H, m, η, Δ, ε, S) satisfies the Hopf identity m ∘ (S ⊗ id) ∘ Δ = η ∘ ε = m ∘ (id ⊗ S) ∘ Δ.

Fields

name: String

Human-readable name.

is_cocommutative: bool

Whether the algebra is cocommutative (Δ = τ ∘ Δ).

antipode_involutive: bool

Whether the antipode is involutive (S² = id).

Implementations

impl HopfAlgebra

pub fn new(name: impl Into<String>) -> Self

Construct a Hopf algebra with the given name.

pub fn group_algebra(group_name: impl Into<String>) -> Self

A group algebra k[G] is a cocommutative Hopf algebra.

pub fn coordinate_ring(group_name: impl Into<String>) -> Self

A commutative Hopf algebra is a coordinate ring O(G) of an affine group.

pub fn antipode_is_involutive(&self) -> bool

The antipode of a commutative or cocommutative Hopf algebra is involutive.

Trait Implementations

impl Clone for HopfAlgebra

fn clone(&self) -> HopfAlgebra

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for HopfAlgebra

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.