invariant theory

Definitions

1. 1

   The branch of algebra concerned with actions of groups on algebraic varieties from the…

   The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions.

   • Invariant theory is the great romantic story of mathematics.[…]In our century, Lie theory and algebraic geometry, differential algebra and algebraic combinatorics are all offsprings of invariant theory.
   • For a linear algebraic group G and a regular representation (#92;rho,V) of G, the basic problem of invariant theory is to describe the G-invariant elements (#123;#92;bigotimes#125;ᵏⱽ)ᴳ of the k-fold tensor product for all k.
2. 2

   Used other than figuratively or idiomatically

   Used other than figuratively or idiomatically: see invariant, theory.

   • The point is that, to construct locally invariant theories, new fields have to be introduced which are referred to as the gauge fields.

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