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.

PlanetMath references:

LieAlgebra

Constructor Summary

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

Method Summary

abstract AbstractComplexSquareMatrix[]	basis() Returns the basis used to represent the Lie algebra.
abstract AbstractComplexSquareMatrix	getElement(AbstractDoubleVector v) Returns an element as a matrix (vector*basis).
abstract AbstractDoubleVector	multiply(AbstractDoubleVector a, AbstractDoubleVector 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 AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)

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

multiply

public abstract AbstractDoubleVector multiply(AbstractDoubleVector a,
                                              AbstractDoubleVector b)

Returns the Lie bracket (commutator) of two elements.

basis

public abstract AbstractComplexSquareMatrix[] basis()

Returns the basis used to represent the Lie algebra.