Editing Invariant theory (section)

{{Short description|Mathematical study of invariants under symmetries
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{{Use American English|date=January 2019}}'''Invariant theory''' is a branch of [[abstract algebra]] dealing with [[Group action (mathematics)|actions]] of [[group (mathematics)|groups]] on [[algebraic variety|algebraic varieties]], such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of [[polynomial function]]s that do not change, or are ''invariant'', under the transformations from a given [[linear group]]. For example, if we consider the action of the [[special linear group]] ''SL<sub>n</sub>'' on the space of ''n'' by ''n'' matrices by left multiplication, then the [[determinant]] is an invariant of this action because the determinant of ''A X'' equals the determinant of ''X'', when  ''A'' is in ''SL<sub>n</sub>''.