About: Representation ring

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In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable.

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  • Der Darstellungsring einer Gruppe ist in der Mathematik vor allem in der Darstellungstheorie, aber auch in Algebra, Topologie und K-Theorie von Bedeutung. (de)
  • In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable. (en)
  • 리 군론에서 표현환(表現環, 영어: representation ring)은 어떤 리 군의 유한 차원 표현들로 생성되는 그로텐디크 환이다. (ko)
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  • Der Darstellungsring einer Gruppe ist in der Mathematik vor allem in der Darstellungstheorie, aber auch in Algebra, Topologie und K-Theorie von Bedeutung. (de)
  • In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable. (en)
  • 리 군론에서 표현환(表現環, 영어: representation ring)은 어떤 리 군의 유한 차원 표현들로 생성되는 그로텐디크 환이다. (ko)
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  • Darstellungsring (de)
  • 표현환 (ko)
  • Representation ring (en)
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