# Subalgebras

### Some articles on subalgebras, subalgebra:

Cartan Subalgebra - Existence and Uniqueness
... Cartan subalgebras exist for finite dimensional Lie algebras whenever the base field is infinite ... and the algebra is finite dimensional then all Cartan subalgebras are conjugate under automorphisms of the Lie algebra, and in particular are all isomorphic ... algebras and generalized Kac–Moody algebras also have Cartan subalgebras ...
Hereditary C*-subalgebra
... In operator algebras, a hereditary C*-subalgebra of a C*-algebra A is a particular type of C*-subalgebra whose structure is closely related to that of A ... A C*-subalgebra B of A is a hereditary C*-subalgebra if for all 0 ≤ a ≤ b, where b ∈ B and a ∈ A, we have a ∈ B ... If a C*-algebra A contains a projection p, then the C*-subalgebra pAp, called a corner, is hereditary ...
Biquaternion - Place in Ring Theory - Subalgebras
... hi, hj, and hk are all plus one, for example, Then the subalgebra given by is ring isomorphic to the plane of split-complex numbers, which has an algebraic structure built upon the unit hyperbola ... The elements hj and hk also determine such subalgebras ... Furthermore, is a subalgebra isomorphic to the tessarines ...
Lie Algebra - Definition and First Properties - Homomorphisms, Subalgebras, and Ideals
... The Lie bracket is not an associative operation in general, meaning that need not equal ... Nonetheless, much of the terminology that was developed in the theory of associative rings or associative algebras is commonly applied to Lie algebras ...
Projective Vector Field - Subalgebras - Killing Algebra
... and hence an affine) and the set of all Killing vector fields on forms a Lie subalgebra of denoted by (the Killing algebra) and satisfies for ...