Artin-Wedderburn isomorphism of $\mathbb{C}[S_3]$
By the Artin - Wedderburn theorem, we know $\mathbb{C}[S_3] \cong \mathbb{C}\oplus \mathbb{C}\oplus Mat_{2x2}(\mathbb{C}) $, and the isomorphism is given by $g \mapsto (1, sgn(g), \rho(g))$, where $ \rho : \mathbb{C}[S_3] \rightarrow Mat_{2x2}(\mathbb{C})$ is a 2-dimensional irreducible representation (permutation representation modulo fixed points). Prove directly that this map is an isomorphism.
152
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment

1.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 882 views
- $12.00
Related Questions
- How to adjust for an additional variable.
- Multiplying Polynomials
- Can enough pizza dough be made to cover the surface of the earth?
- Certain isometry overfinite ring is product of isometries over each local factor
- How old is the wise man?
- Determine the Closed Form of a Recurrance Relation
- Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)-x, e^{y \sin z})$. Compute the derivative matrix $Df$.
- Prove that $tan x +cot x=sec x csc x$