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Lie Groups and Subsemigroups with Surjective Exponential Function

Karl Heinrich HofmannWolfgang Ruppert

出版	American Mathematical Soc., 1997
主題	Mathematics / Algebra / GeneralMathematics / Group TheoryMathematics / Topology
ISBN	08218064169780821806418
URL	http://books.google.com.hk/books?id=u4XTCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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 nature 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 (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.