Definition

Direct Sum of Representations

Lie Groups and Lie Algebras · lie-groups.tex

Given $G$-representations $(V, \rho)$ and $(W, \sigma)$ (Definition~Group Representation), their direct sum is $(V \oplus W, \rho \oplus \sigma)$ where $(\rho \oplus \sigma)(g)(v, w) = (\rho(g)v, \sigma(g)w)$.

Depends on

Representation

Used in

Complete Reducibility
Proposition

Dependency Graph

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