jsci.maths.algebras

Class su2Dim3

java.lang.Object

jsci.maths.algebras.LieAlgebra

jsci.maths.algebras.su2Dim3

public final class su2Dim3
extends LieAlgebra

The su2Dim3 class encapsulates su(2) algebras using the 3 dimensional (adjoint) representation. Elements are represented by 3-vectors with a matrix basis.

Method Summary

Modifier and Type	Method and Description
AbstractComplexSquareMatrix[]	basis() Returns the basis used to represent the Lie algebra.
AbstractDoubleSquareMatrix	cartanMetric() Returns the Cartan metric.
AbstractComplexSquareMatrix	getElement(AbstractDoubleVector v) Returns an element as a matrix (vector*basis).
static su2Dim3	getInstance() Singleton.
double	killingForm(AbstractDoubleVector a, AbstractDoubleVector b) Returns the Killing Form of two elements (scalar product).
AbstractDoubleVector	multiply(AbstractDoubleVector a, AbstractDoubleVector b) Returns the Lie bracket (commutator) of two elements.

Methods inherited from class jsci.maths.algebras.LieAlgebra

toString

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Method Detail

getInstance

public static final su2Dim3 getInstance()

Singleton.

getElement

public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)

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

Specified by:

getElement in class LieAlgebra

multiply

public AbstractDoubleVector multiply(AbstractDoubleVector a,
                                     AbstractDoubleVector b)

Returns the Lie bracket (commutator) of two elements. Same as the vector cross product.

Specified by:

multiply in class LieAlgebra

killingForm

public double killingForm(AbstractDoubleVector a,
                          AbstractDoubleVector b)

Returns the Killing Form of two elements (scalar product).

basis

public AbstractComplexSquareMatrix[] basis()

Returns the basis used to represent the Lie algebra.

Specified by:

basis in class LieAlgebra

cartanMetric

public AbstractDoubleSquareMatrix cartanMetric()

Returns the Cartan metric.