English Dictionary

invariant theory

名詞

可算名詞 不可算名詞

(algebra, representation theory) The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions.

日本語の意味

不変理論：代数学の一分野で、群の作用が代数多様体に及ぼす影響を、関数への効果という観点から解析する理論

Graduate students often encounter invariant theory when learning how group actions affect functions on algebraic varieties.

大学院生は、群が代数多様体上で作用し、その作用が関数に与える影響を扱う代数学の分野である不変式論に触れることがよくある。

意味（1）

(algebra, representation theory) The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions.

Today, invariant theory is often understood as a branch of representation theory, algebraic geometry, commutative algebra, and algebraic combinatorics. Each of these four disciplines has roots in nineteenth-century invariant theory. […] In modern terms, the basic problem of invariant theory can be categorized as follows. Let V be a K-vector space on which a group G acts linearly. In the ring of polynomial functions K[V] consider the subring K[V]ᴳ consisting of all polynomial functions on V which are invariant under the action of the group G. The basic problem is to describe the invariant ring K[V]ᴳ. In particular, we would like to know whether K[V]ᴳ is finitely generated as a K-algebra and, if so, to give an algorithm for computing generators.

意味（2）

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.

invariant theories （ plural ）