Talk: Relative K1-Gruppe
meta
default Notation
is a ring, unital but not necessary commutative- Ideals are assumed to be two-sided, unless stated otherwise
other notes
- I follow the numbers of the script
- In these notes, I may write alternative (categorical) proofs and I will
Motivation
We want to construct long exact sequence
Hence we will also need a notion of relative 
This gives us further tools to compute 
(by restricting the possiblilities).
Furthermore we may use powerful tools of homological algebra, especially the Five-Lemma / Four-Lemma of modules of monomorphisms / Four-Lemma of modules of epimorphisms
This comes at the cost of being a "worse" invariant.
Aspects
Reminder
7.2
7.3
- natural transformation from elementary linear group to general linear group
- natural transformation from infinite elementary linear group to general linear group
- exact diagram of infinite general linear groups and elementary linear groups
- relative infinite elementary linear group as normal subgroup
- explicite description of the relative elementary linear group