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About: Representation ring     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatFiniteGroups, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: anatomical structureyago:WikicatLieGroupsyago:Abstraction100002137yago:Group100031264yago:WikicatFiniteGroups New Facet based on Instances of this Class

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.