org.jscience.mathematics.algebraic.algebras
Class su2Dim3

java.lang.Object
  extended by org.jscience.mathematics.algebraic.algebras.LieAlgebra
      extended by org.jscience.mathematics.algebraic.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
 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 (vectorbasis).
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 org.jscience.mathematics.algebraic.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.

Returns:
DOCUMENT ME!

getElement

public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)
Returns an element as a matrix (vectorbasis).

Specified by:
getElement in class LieAlgebra
Parameters:
v - DOCUMENT ME!
Returns:
DOCUMENT ME!

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
Parameters:
a - DOCUMENT ME!
b - DOCUMENT ME!
Returns:
DOCUMENT ME!
Throws:
IllegalDimensionException - DOCUMENT ME!

killingForm

public double killingForm(AbstractDoubleVector a,
                          AbstractDoubleVector b)
Returns the Killing Form of two elements (scalar product).

Parameters:
a - DOCUMENT ME!
b - DOCUMENT ME!
Returns:
DOCUMENT ME!

basis

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

Specified by:
basis in class LieAlgebra
Returns:
DOCUMENT ME!

cartanMetric

public AbstractDoubleSquareMatrix cartanMetric()
Returns the Cartan metric.

Returns:
DOCUMENT ME!