Direct Limits of Diagonal Chains of Type O, U, and Sp, and Their Homotopy Groups

ABSTRACT

Baranov and Zhilinskii (1999) have shown a classification theorem for diagonal direct limits of simple Lie algebras. In this work, we will transfer their results to diagonal direct limits of certain matrix groups, and show that homotopy groups are significant invariants for specific classes of direct limit groups.

Communicated by B. Allison

Keywords:

• Direct limit
• Homotopy groups
• Lie algebra
• Lie group

Mathematics Subject Classification:

• Primary 22E15
• Secondary 22E65

ACKNOWLEDGMENT

This work is based on my diploma thesis, which I wrote at the Technical University of Darmstadt in 2003. I would like to thank my supervisor Prof. K. H. Neeb for suggesting the topic and for many helpful discussions.