Crate lie_groups 

Lie groups and Lie algebras for computational mathematics.

This crate provides concrete implementations of the classical Lie groups used in physics and geometry, with emphasis on correctness, numerical stability, and ergonomic APIs.

Implemented Groups

Group	Algebra	Representation	Dimension
U1	U1Algebra	Phase (complex unit)	1
SU2	Su2Algebra	2×2 complex unitary	3
SO3	So3Algebra	3×3 real orthogonal	3
SU3	Su3Algebra	3×3 complex unitary	8
SUN<N>	SunAlgebra<N>	N×N complex unitary	N²−1
RPlus	RPlusAlgebra	Positive reals	1

Trait Abstractions

The LieGroup and LieAlgebra traits provide a uniform interface:

use lie_groups::{LieGroup, LieAlgebra, SU2, Su2Algebra};

let g = SU2::identity();
let h = SU2::exp(&Su2Algebra::new([0.1, 0.2, 0.3]));
let gh = g.compose(&h);
let inv = h.inverse();

Features

• Quaternion-optimized SU(2): Rotation operations via unit quaternions
• Baker-Campbell-Hausdorff: Lie algebra composition up to 5th order
• Root systems: Type Aₙ (other families planned)
• Representation theory: Casimir operators, characters, Clebsch-Gordan
• Numerical stability: Conditioned logarithms, scaling-and-squaring exp

Re-exports

pub use bch::bch_checked;

pub use bch::bch_error_bound;

pub use bch::bch_fifth_order;

pub use bch::bch_fourth_order;

pub use bch::bch_is_practical;

pub use bch::bch_safe;

pub use bch::bch_second_order;

pub use bch::bch_split;

pub use bch::bch_third_order;

pub use bch::bch_will_converge;

pub use bch::BchError;

pub use bch::BchMethod;

pub use error::ConditionedLogResult;

pub use error::LogCondition;

pub use error::LogError;

pub use error::LogQuality;

pub use error::LogResult;

pub use error::RepresentationError;

pub use error::RepresentationResult;

pub use quaternion::UnitQuaternion;

pub use representation::casimir::Casimir;

pub use representation::su3_irrep::Su3Irrep;

pub use representation::character;

pub use representation::character_su2;

pub use representation::clebsch_gordan_decomposition;

pub use representation::Spin;

pub use root_systems::Alcove;

pub use root_systems::CartanSubalgebra;

pub use root_systems::Root;

pub use root_systems::RootSystem;

pub use root_systems::WeightLattice;

pub use root_systems::WeylChamber;

pub use rplus::RPlus;

pub use rplus::RPlusAlgebra;

pub use so3::So3Algebra;

pub use so3::SO3;

pub use su2::Su2Algebra;

pub use su2::SU2;

pub use su3::Su3Algebra;

pub use su3::SU3;

pub use sun::SU2Generic;

pub use sun::SU3Generic;

pub use sun::SunAlgebra;

pub use sun::SU4;

pub use sun::SU5;

pub use sun::SUN;

pub use traits::Abelian;

pub use traits::AntiHermitianByConstruction;

pub use traits::Compact;

pub use traits::LieAlgebra;

pub use traits::LieGroup;

pub use traits::SemiSimple;

pub use traits::Simple;

pub use traits::TracelessByConstruction;

pub use u1::U1Algebra;

pub use u1::U1;

Modules

bch

Baker-Campbell-Hausdorff (BCH) Formula

error

Error types for Lie group and Lie algebra operations

quaternion

Quaternionic Formulation of SU(2)

representation

Representation theory for Lie groups and Lie algebras.

root_systems

Root Systems for Semisimple Lie Algebras

rplus

ℝ⁺: The Positive Reals (Multiplicative Scaling Group)

so3

Lie group SO(3) - 3D rotation group

su2

SU(2): The Special Unitary Group in 2 Dimensions

su3

Lie group SU(3) - Special unitary 3×3 group

sun

Generic SU(N) - Special unitary N×N matrices

traits

Traits for Lie groups and Lie algebras.

u1

U(1): The Circle Group