K-Theory Spectrum

In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum ${\displaystyle K_R}$ whose nth term is given by, writing ${\displaystyle \mathrm{\Sigma }R}$ for the suspension of R,

${\displaystyle (K_R{)}_n=K_0({\mathrm{\Sigma }}^{n}R)\times BGL({\mathrm{\Sigma }}^{n}R{)}^{+}}$,

where "+" means the Quillen's + construction.^[1] By definition, ${\displaystyle K_i(R)={\pi }_i(K_R)}$.

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/K-theory spectrum. Read more