JSci.maths.algebras

Class LieAlgebra

java.lang.Object

JSci.maths.algebras.LieAlgebra

Direct Known Subclasses:

so3_1Dim4, sp2_RDim2, sp2_RDim3, su2Dim2, su2Dim3, su3Dim3

public abstract class LieAlgebra
extends java.lang.Object

The LieAlgebra class provides an abstract encapsulation for Lie algebras. Elements are represented by vectors with a matrix basis.

Version:

1.2

Author:

Mark Hale

Constructor Summary

Constructors

Constructor and Description
LieAlgebra(java.lang.String aLabel) Constructs a Lie algebra.

Method Summary

Methods

Modifier and Type	Method and Description
abstract ComplexSquareMatrix[]	basis() Returns the basis used to represent the Lie algebra.
abstract ComplexSquareMatrix	getElement(DoubleVector v) Returns an element as a matrix (vector*basis).
abstract DoubleVector	multiply(DoubleVector a, DoubleVector b) Returns the Lie bracket (commutator) of two elements.
java.lang.String	toString() Returns a string representing this algebra.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

LieAlgebra

public LieAlgebra(java.lang.String aLabel)

Constructs a Lie algebra.

Parameters:

aLabel - a label that identifies this algebra

Method Detail

toString

public final java.lang.String toString()

Returns a string representing this algebra.

Overrides:

toString in class java.lang.Object

getElement

public abstract ComplexSquareMatrix getElement(DoubleVector v)

Returns an element as a matrix (vector*basis).

multiply

public abstract DoubleVector multiply(DoubleVector a,
                    DoubleVector b)

Returns the Lie bracket (commutator) of two elements.

basis

public abstract ComplexSquareMatrix[] basis()

Returns the basis used to represent the Lie algebra.