Lie Groups and Subsemigroups with Surjective Exponential Function (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Hofmann, Karl Heinrich; Ruppert, Wolfgang A.F.

Softcover

ISBN 10: 0821806416 ISBN 13: 9780821806418

Publisher: American Mathematical Society, 1998

Synopsis

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under natural reductions setting aside the 'group part' of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are $SL(2,R)$ and its universal covering group, almost abelian solvable Lie groups (i.e., vector groups extended by homotheties), and compact Lie groups.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1998
• Language: English
• ISBN 10: 0821806416
• ISBN 13: 9780821806418
• Binding: Paperback
• Number of pages: 174