The existence of a semialgebraic continuous factorization map for some compact linear groups

TL;DR

This paper proves that certain compact linear groups can be continuously and semialgebraically mapped onto real vector spaces, establishing a new understanding of their structure.

Contribution

It demonstrates the existence of semialgebraic continuous factorization maps for specific compact linear groups, a novel result in the field.

Findings

Existence of semialgebraic continuous maps for certain groups

Maps onto real vector spaces established

Advances understanding of group structure and mappings

Abstract

It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.