Notes on "Theory of Lie Groups" by Chevalley
Errata
So far these are just typos but they may cause some confusion.
The book uses a mixture of British (neighbourhood) and American (center) spellings.
The Roman numerals refer to the first twelve pages of the book, some of which are unnumbered. The page of notations is thus page xii.
Page xii: \(\delta p\sigma\) should be Sp \(\sigma\). This seems to be an error by the typesetter. The trace of the matrix is labelled "Sp" throughout the book. "Sp" is an abbreviation of the German "Spur".
Page xii: \(\cup, \cap\) should be \(\cap, \cup\).
Page xii: \(\epsilon\) confusion. The book uses both \(\varepsilon\) and \(\epsilon\) to mean set membership, but also uses \(\epsilon\) for the neutral (identity) element, the identity matrix.
Page xii: Hausdorf should be Hausdorff.
Page 9: othogonal should be orthogonal.
Notations
This is a mini dictionary of terms that Chevalley uses, and the terms which seem to be more common these days.
- \(]a,b[\)
- \((a,b)\). Chevalley uses reversed [] for open intervals
- Adherence
- Closure
- Characteristic root
- Eigenvalue. Chevalley does not use "eigenvalue", but he uses the term "eigenvectors", see for example page 13.
- Distinguished subgroup
- Normal subgroup
- Neutral element
- Identity element
- Permutable matrices
- Commuting matrices. Chevalley also refers to abelian matrices.
- Regular matrix
- Nonsingular or invertible matrix