𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exponential Radicals of Solvable Lie Groups

✍ Scribed by D.V. Osin

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
127 KB
Volume
248
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

For any connected Lie group G, we introduce the notion of exponential radical Exp G that is the set of all strictly exponentially distorted elements of G. In case G is a connected simply-connected solvable Lie group, we prove that Exp G is a connected normal Lie subgroup in G and the exponential radical of the quotient group G/Exp(G) is trivial. Using this result, we show that the relative growth function of any subgroup in a polycyclic group is either polynomial or exponential.

πŸ“œ SIMILAR VOLUMES

Weakly Exponential Lie Groups
Weakly Exponential Lie Groups
✍ Karl-Hermann Neeb πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 314 KB
On Surjectivity of the Power Maps of Sol
On Surjectivity of the Power Maps of Solvable Lie Groups
✍ Pralay Chatterjee πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 158 KB

In this paper we study surjectivity of the map g β†’ g n on an arbitrary connected solvable Lie group and describe certain necessary and sufficient conditions for surjectivity to hold. The results are applied also to study the exponential maps of the Lie groups.  2002 Elsevier Science (USA)

Remarks on Gelfand Pairs Associated to N
Remarks on Gelfand Pairs Associated to Non-Type-I Solvable Lie Groups
✍ Katsuhiko Kikuchi πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 323 KB

dedicated to professor takeshi hirai on his 60th birthday Let S be a connected and simply connected unimodular solvable Lie group and K a connected compact Lie group acting on S as automorphisms. We call the pair (K ; S) a Gelfand pair if the Banach V-algebra L 1 K (S) of all K-invariant integrable

Historical Remarks on the Surjectivity o
Historical Remarks on the Surjectivity of the Exponential Function of Lie Groups
✍ Michael WΓΌstner πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 82 KB

In 1892, F. Engel and E. Study investigated the exponential map of classical Lie groups for the first time. They showed that the special projective Lie groups over C possess surjective exponential functions. Engel also gave a "proof" for the corresponding claims for the other projective classical gr