A "normal subalgebra" is a term used in mathematics to refer to a specific type of subalgebra that is an invariant under conjugation by elements of the algebra it is a part of. Some synonyms for "normal subalgebra" include "invariant subalgebra," "conjugacy-closed subalgebra," and "conjugacy-invariant subalgebra." Another term that is commonly used is "centralizer," which refers to the set of all elements in the algebra that commute with the elements of the subalgebra. Additionally, "regular subalgebra" is another synonym used to refer to a subalgebra that is an invariant under an automorphism of the algebra. Overall, these synonyms help to describe and define the properties of normal subalgebras in a mathematical context.