For , define to be the free abelian group on symbols for distinct integers between and , and , subject to the following relations:
Note that if denotes the elementary matrix with one along the diagonal, and in the entry, then the also satisfy the above relations, giving a well defined morphism , where the latter is the group of elementary matrices.
Taking a colimit over gives the Steinberg group . The importance of the Steinberg group is that the kernel of the map is the second algebraic -group of the ring , . This also coincides with the kernel of the Steinberg group. One can also show that the Steinberg group is the universal central extension of the group .
|Date of creation||2013-03-22 16:44:38|
|Last modified on||2013-03-22 16:44:38|
|Last modified by||dublisk (96)|