Algebra theory MOC

Trace form

Let (𝐴, ⋅) be an algebra over 𝕂 and 𝜌 :𝐴 →𝑉 be a finite-dimensional representation of 𝜌. The trace form is the bilinear form on 𝐴 defined by¹ falg

⟨𝑥,𝑦⟩𝜌=tr𝜌⁡(𝑥,𝑦)=tr⁡(𝜌(𝑥)𝜌(𝑦))

for 𝑥,𝑦 ∈𝐴.

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tidy | en | SemBr

Footnotes

1. Note the product of the algebra might not be represented as composition in the representation, e.g. for a Lie algebra representation. ↩