Lie groups and subsemigroups with surjective exponential function
著者
書誌事項
Lie groups and subsemigroups with surjective exponential function
（Memoirs of the American Mathematical Society, no. 618）
American Mathematical Society, 1997
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注記
"November 1997, volume 130, number 618 (second of 4 numbers)"
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Introduction The basic theory of exponential semigroups in Lie groups Weyl groups and finiteness properties of Cartan subalgebras Lie semialgebras More examples Test algebras and groups Groups supporting reduced weakly exponential semigroups Roots and root spaces Appendix: The hyperspace of a locally compact space References Index.
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