What are the main types of algebra?
Algebraic data type
Two common classes of algebraic types are product types (i.e., tuples and records) and sum types (i.e., tagged or disjoint unions or "variant types").
Reductive Lie algebra
The most basic example is the Lie algebra formula_2 of formula_3 matrices with the commutator as Lie bracket, or more abstractly as the endomorphism algebra of an "n"-dimensional vector space, formula_4 This is the Lie algebra of the general linear group GL("n"), and is reductive as it decomposes as formula_5 corresponding to traceless matrices and scalar matrices.