JSci.maths.groups
Class LieGroup

java.lang.Object
  JSci.maths.groups.LieGroup

Direct Known Subclasses:

U1

public class LieGroup
extends java.lang.Object

The LieGroup class provides an encapsulation for Lie groups. Elements are represented by complex matrices, and are limited to being near the identity.

PlanetMath references:

LieGroup

Constructor Summary

LieGroup(AbstractComplexSquareMatrix[] gens)
Constructs a Lie group from a Lie algebra.

Method Summary

int	dimension() Returns the dimension of the group.
AbstractComplexSquareMatrix	getElement(AbstractDoubleVector v) Returns an element near the identity.
AbstractComplexSquareMatrix	identity() Returns the identity element.
boolean	isIdentity(AbstractComplexSquareMatrix a) Returns true if the element is the identity element of this group.
boolean	isInverse(AbstractComplexSquareMatrix a, AbstractComplexSquareMatrix b) Returns true if one element is the inverse of the other.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LieGroup

public LieGroup(AbstractComplexSquareMatrix[] gens)

Constructs a Lie group from a Lie algebra.

Parameters:

gens - the group generators

Method Detail

dimension

public final int dimension()

Returns the dimension of the group.

getElement

public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v)

Returns an element near the identity.

Parameters:

v - a small element from the Lie algebra

identity

public AbstractComplexSquareMatrix identity()

Returns the identity element.

isIdentity

public final boolean isIdentity(AbstractComplexSquareMatrix a)

Returns true if the element is the identity element of this group.

Parameters:

a - a group element

isInverse

public final boolean isInverse(AbstractComplexSquareMatrix a,
                               AbstractComplexSquareMatrix b)

Returns true if one element is the inverse of the other.

Parameters:

a - a group element

b - a group element