Math 2.0

Concept

Defined over

Summary

Given a field extension K/FK/F, a representation V of a group G over K is said to be defined over F if V≃V0⊗FKV \simeq V_0 \otimes_F K for some representation V0V_0 over F such that g:V→Vg: V \to V is induced by g:V0→V0g: V_0 \to V_0; i.e., g⋅(v⊗λ)=gv⊗λg \cdot (v \otimes \lambda) = g v \otimes \lambda. Here, V0V_0 is called an F-form of V (and is not necessarily unique).

Further reading

  1. Wikipedia, page 55799101, revision 1351912484, Glossary of representation theory, section D. adopted
About this page
TagJEMV9NEDGR
URIm2://JEMV9NEDGR
Kindconcept
WritingW1 stated
Changed5 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge defines in: at least one definition (0 of 1)
  • edge instance_of in: at least two examples (0 of 2)
  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.