[jdwg]

The direct sum decomposition you mention doesn't always happen, as you can see in some of the examples in the calculator. It is closer to happening when \gamma is zero, and if \gamma is zero and we switch from integer coefficient to field coefficients, then it always happens!

[082349872349872]

obviously I need to play with the calculator more (and probably work the exercises) ... hope you don't mind if I get back to you with more Q's once I have them.

[jdwg]

well, I love the subject, so I'm glad to discuss whatever! And let me know if all of the exercises are too hard. There should always be a couple of easy ones, but I don't know this audience very well.