Interface LieAlgebra<E,S>

All Superinterfaces:
AbelianGroup<E>, AbelianMonoid<E>, Algebra<E,S>, Group<E>, Magma<E>, Module<E,S>, Monoid<E>, Ring<E>, Semiring<E>, Set<E>
All Known Implementing Classes:
MatrixLieAlgebra
public interface LieAlgebra<E,S> extends Algebra<E,S>
Represents a Lie Algebra.

A Lie Algebra is an algebra where the product (Lie bracket) satisfies:

  • Bilinearity
  • Alternativity: [x, x] = 0
  • Jacobi Identity: [x, [y, z]] + [y, [z, x]] + [z, [x, y]] = 0

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • bracket

      default E bracket(E a, E b)
      Returns the Lie bracket [a, b].

      This corresponds to the Algebra.multiply(Object, Object) method of the Algebra interface.

      Parameters:
      a - the first element
      b - the second element
      Returns:
      [a, b]