Difference between revisions of "Blocks"
(Created page with "== Blocks == Unless stated otherwise, blocks of a finite group <math>G</math> will be indecomposable two-sided ideals of <math>kG</math>. In some situations it will be the co...") |
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== Blocks == | == Blocks == | ||
| − | Unless stated otherwise, blocks of a finite group <math>G</math> will be indecomposable two-sided ideals of <math>kG</math>. In some situations it will be the corresponding block of <math>\mathcal{O}G</math>. | + | Unless stated otherwise, blocks of a finite group <math>G</math> will be indecomposable two-sided ideals that are direct summands of <math>kG</math>. In some situations it will be the corresponding block of <math>\mathcal{O}G</math>. |
<math>B_0(A)</math> will denote the principal block of an algebra <math>A</math>. However we often use the notation of [http://www.math.rwth-aachen.de/~MOC/decomposition/| GAP] to label blocks of certain groups, where the principal block is usually labelled <math>B_1(kG)</math>. | <math>B_0(A)</math> will denote the principal block of an algebra <math>A</math>. However we often use the notation of [http://www.math.rwth-aachen.de/~MOC/decomposition/| GAP] to label blocks of certain groups, where the principal block is usually labelled <math>B_1(kG)</math>. | ||
Latest revision as of 15:05, 14 September 2026
Blocks
Unless stated otherwise, blocks of a finite group [math]G[/math] will be indecomposable two-sided ideals that are direct summands of [math]kG[/math]. In some situations it will be the corresponding block of [math]\mathcal{O}G[/math].
[math]B_0(A)[/math] will denote the principal block of an algebra [math]A[/math]. However we often use the notation of GAP to label blocks of certain groups, where the principal block is usually labelled [math]B_1(kG)[/math].
