Weakening the topology of a Lie group
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- by T. Christine Stevens PDF
- Trans. Amer. Math. Soc. 276 (1983), 541-549 Request permission
Abstract:
With any topological group $(G, \mathcal {U})$ one can associate a locally arcwise-connected group $(G, {\mathcal {U}}^{\ast })$, where ${\mathcal {U}}^{\ast }$ is stronger than $\mathcal {U}$. $(G, \mathcal {U})$ is a weakened Lie $(WL)$ group if $(G, {\mathcal {U}}^{\ast })$ is a Lie group. In this paper the author shows that the WL groups with which a given connected Lie group $(L,\mathcal {J})$ is associated are completely determined by a certain abelian subgroup $H$ of $L$ which is called decisive. If $L$ has closed adjoint image, then $H$ is the center $Z(L)$ of $L$; otherwise, $H$ is the product of a vector group $V$ and a group $J$ that contains $Z(L)$. $J/Z(L)$ is finite (trivial if $L$ is solvable). We also discuss the connection between these theorems and recent results of Goto.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 276 (1983), 541-549
- MSC: Primary 22E20; Secondary 22A05, 22E15
- DOI: https://doi.org/10.1090/S0002-9947-1983-0688961-1
- MathSciNet review: 688961