The Hattori-Stallings trace over a unit ring 
sends an idempotent matrix 
to its diagonal sum modulo additive commutators.
Writing ![[R,R]_(add)](/images/equations/Hattori-StallingsTrace/Inline3.svg)
for the additive subgroup generated by 
for 
,
its value is
![HS(e)=sum_(i=1)^qe_(ii) (mod[R,R]_(add)).](/images/equations/Hattori-StallingsTrace/NumberedEquation1.svg) |
It depends only on the associated finitely generated projective module and extends
additively to a map on 
in algebraic K-theory.
For the complex discrete group algebra 
, its conjugacy-class coordinates are
 |
The sums converge absolutely, and 
ranges over conjugacy classes in 
. The l1-Bass
conjecture predicts finite support
on conjugacy classes of elements
of finite order. Finite order refers to the elements, not to the cardinality
of their conjugacy classes.
