Michi’s blog » archive for June, 2006

## Group cohomology revisited: Quaternionic unit group

• June 20th, 2006
• 9:54 am

In a previous installment, we calculated with some amount of success. For that post, I said that I was going to calculate the cohomologies of and of by hand – and I’ve been at it for the latter group since then. With some help from my advisor – mainly with executing the obvious algorithms far enough that I get decent material to work with – I know have it.

## The group

So, for starters, we need a presentation of such that we can work well with it. We all know that . So due to ij=-k and , we can just pick any two of the i,j,k and call them x and y. Then , and iji=ik=j so xyx=y. This gives us the presentation

• June 19th, 2006
• 3:13 pm

This blog just migrated to WP 2.0. Should anything be odd, please notify me.

The migration was to a large portion motivated by commenting problems I’ve been told about. I hope that my readers out there will be able to comment now; possibly even without logging in!

## Weekly Report: Power tourism

• June 18th, 2006
• 11:15 am

It’s been a while since I managed to write one of these. The reason is simple enough – my weekends have been packed; and I don’t get around to it during the weeks.

During the last three weekends, first my parents and my brother, and then for the last two and the week inbetween my fiancĂ©e, have been visiting me in Jena. Thus, I have covered more ground in these three weeks when it comes to tourism than I probably will be able to do in several months. I have seen the Blue Man Group in Berlin (WOW!), I have seen the Dornburg, the Feengrotten and Weimar. I have eaten at the expensive luxurious restaurant at the top of the old university tower in Jena (it’s bloody scary, but quite cool – the restaurant is on the 29th floor; in a city where only one single house goes above 10 floors).

## More group cohomology

• June 8th, 2006
• 10:10 pm

My advisor told me to go hit and as my next two cohomology calculation projects; try to do them with resolutions by hand so that I get a feeling for what’s going on. After failing spectacularily both at getting a resolution of with , he walked me through his Shiny! Gr