Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
JOURNAL OF LIE THEORY, cilt.25, sa.3, ss.753-774, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 25 Sayı: 3
- Basım Tarihi: 2015
- Dergi Adı: JOURNAL OF LIE THEORY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.753-774
- Yıldız Teknik Üniversitesi Adresli: Hayır
Özet
For a finite dimensional connected Lie group G with Lie algebra g, we consider a Lie-generating Lie wedge W subset of g. If S is a Lie subsemigroup of G with subtangent wedge W we give sufficient conditions for S to be free on small enough local semigroups U boolean AND S in the sense that continuous local homomorphisms extend to global ones on S. The constructions involve developing a homotopy theory of U boolean AND S-directed paths. We also consider settings where the free construction leads to a simply connected covering of S.