- Commit
- 238d43d057209dd9e5a584d35286cf3284c19402
- Parent
- 4f800549d96246c5cdde1b5fcc18b8437dfc6374
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed a typo
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Fixed a typo
1 file changed, 1 insertion, 1 deletion
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/complete-reducibility.tex | 2 | 1 | 1 |
diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex @@ -86,7 +86,7 @@ this is not always the case. For instance\dots is a representation of the Lie algebra \(K[x]\). Notice \(V\) has a single nonzero proper subrepresentation, which is spanned by the vector \((1, 0)\). This is because if \((a + b, b) = \rho(x) \ (a, b) = \lambda (a, b)\) for - some \(\lambda \in \mathbb{C}\) then \(\lambda = 1\) and \(b = 0\). Hence \(V\) is + some \(\lambda \in K\) then \(\lambda = 1\) and \(b = 0\). Hence \(V\) is indecomposable -- it cannot be broken into a direct sum of 1-dimensional subrepresentations -- but it is evidently not irreducible. \end{example}