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# Class JSci.maths.algebras.LieAlgebra

    java.lang.Object
       |
       +----JSci.maths.algebras.LieAlgebra

public abstract class LieAlgebra
extends Object

The LieAlgebra class provides an abstract encapsulation for Lie algebras. Elements are represented by vectors with a matrix basis.

##

LieAlgebra(String)
  Constructs a Lie algebra.

##

basis()
  Returns the basis used to represent the Lie algebra.
getElement(DoubleVector)
  Returns an element as a matrix (vector*basis).
multiply(DoubleVector, DoubleVector)
  Returns the Lie bracket (commutator) of two elements.
toString()
  Returns a string representing this algebra.

##

LieAlgebra

     public LieAlgebra(String aLabel)

  Constructs a Lie algebra.

  Parameters:
    aLabel - a label that identifies this algebra

##

toString

     public final String toString()

  Returns a string representing this algebra.

  Overrides:
    toString in class Object

getElement

     public abstract ComplexSquareMatrix getElement(DoubleVector v)

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

multiply

     public abstract DoubleVector multiply(DoubleVector a,
                                           DoubleVector b)

  Returns the Lie bracket (commutator) of two elements.

basis

     public abstract ComplexSquareMatrix[] basis()

  Returns the basis used to represent the Lie algebra.

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