On the Non-Commutativity of Pontrjagin Rings Mod 3 of Some Compact Exceptional Groups

Abstract

Pontrjagin rings over the field of rational numbers of compact Lie groups are commutative in the sense of graded algebras (or anti-commutative in the classical terminology) [14]. Pontrjagin rings over the field Z_p (p 0) of several compact simple Lie groups were studied by Borel [5]. The most examples are commutative. However, this is generally not true.