JSci.maths.algebras
Class su2Dim3

java.lang.Object
  extended by JSci.maths.algebras.LieAlgebra
      extended by 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.

Version:
1.2
Author:
Mark Hale

Method Summary
 ComplexSquareMatrix[] basis()
          Returns the basis used to represent the Lie algebra.
 DoubleSquareMatrix cartanMetric()
          Returns the Cartan metric.
 ComplexSquareMatrix getElement(DoubleVector v)
          Returns an element as a matrix (vector*basis).
static su2Dim3 getInstance()
          Singleton.
 double killingForm(DoubleVector a, DoubleVector b)
          Returns the Killing Form of two elements (scalar product).
 DoubleVector multiply(DoubleVector a, DoubleVector 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
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Method Detail

getInstance

public static final su2Dim3 getInstance()
Singleton.


getElement

public ComplexSquareMatrix getElement(DoubleVector v)
Returns an element as a matrix (vector*basis).

Specified by:
getElement in class LieAlgebra

multiply

public DoubleVector multiply(DoubleVector a,
                             DoubleVector 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(DoubleVector a,
                          DoubleVector b)
Returns the Killing Form of two elements (scalar product).


basis

public ComplexSquareMatrix[] basis()
Returns the basis used to represent the Lie algebra.

Specified by:
basis in class LieAlgebra

cartanMetric

public DoubleSquareMatrix cartanMetric()
Returns the Cartan metric.