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# Class JSci.maths.algebras.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.

##

su2Dim3()
  Constructs an su(2) algebra.

##

basis()
  Returns the basis used to represent the Lie algebra.
cartanMetric()
  Returns the Cartan metric.
getElement(DoubleVector)
  Returns an element as a matrix (vector*basis).
killingForm(DoubleVector, DoubleVector)
  Returns the Killing Form of two elements (scalar product).
multiply(DoubleVector, DoubleVector)
  Returns the Lie bracket (commutator) of two elements.

##

su2Dim3

     public su2Dim3()

  Constructs an su(2) algebra.

##

getElement

     public ComplexSquareMatrix getElement(DoubleVector v)

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

  Overrides:
    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.

  Overrides:
    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.

  Overrides:
    basis in class LieAlgebra

cartanMetric

     public DoubleSquareMatrix cartanMetric()

  Returns the Cartan metric.

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