Primary School Arithmetic and Group Cohomology

Mathematics under the Microscope

[Originally published on Blogger, Monday, August 28, 2006]

In Molier’s Le bourgeois gentilhomme, Monsieur Jourdain was surprised to learn that he had been speaking prose all his life. I was recently reminded (by Mikael Johanssons’ blog) that all my life I was calculating 2-cocycles. Indeed, a carry in elementary arithmetic, a digit that is transferred from one column of digits to another column of more significant digits during addition of two decimals, is defined by the rule   

c(a,b) =1 if a+b >9 and =0 otherwise.

One can easily check that this is a 2-cocycle from Z/10Z to Z and is responsible for the extension of additive groups

0 -> 10Z -> Z -> Z/10Z ->….
Of course, what else it could be?

View original post 179 more words

Advertisements

About isomorphismes

Argonaut: someone engaged in a dangerous but potentially rewarding adventure.
This entry was posted in Uncategorized. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s