See Representation theory of semisimple Lie algebras. Most algebraic structures are examples of universal algebras. Such Lie algebras are called abelian, cf. Nearly all well-known algebraic structures other than Boolean algebras are undecidable. Moreover, every Lie group homomorphism induces a homomorphism between the corresponding Lie algebras. Skew polynomial rings are closely related to crossed product algebras. Examples include matrix algebras and quaternion algebras. All finite Boolean algebras are complete. For further detail about the geometrical uses of Clifford algebras, see Geometric algebra. Let be a morphism of Heyting algebras. The Quaternions can be generalized into further algebras called "quaternion algebras". There are also the isomorphisms of the Lie algebras and . The Pauli matrices abide by the physicists' convention for Lie algebras. A similar interpretation is possible for quaternions and Clifford algebras in general. See also semidirect sum of Lie algebras.