Negative K-Theory of Generalized Quaternion Groups and Binary Polyhedral Groups

Abstract

Classical group representation theory is used to determine which finite groups have finite negative K-theory. There follows a computation of the K ₋₁ of integral group rings ZG for all finite non-abelian subgroups of the group SU(2) of unit quaternions. In principle, the method applies to any finite group.

Key Words:

• Binary polyhedral group
• CP-group
• Group ring
• Lower K-theory
• Negative K-theory
• Quaternion

2010 Mathematics Subject Classification:

• Primary 19D35
• Secondary 20C11, 20E45, 20F50

Notes

Communicated by S. Sehgal.