The fixed set of the inverse involution on a Lie group
Haibao Duan, Shali Liu
TL;DR
This paper develops a general method to determine the structure of the fixed set of the inverse involution in a Lie group, extending previous work on centralizers of elements.
Contribution
It introduces a systematic procedure for calculating the isomorphism type of the fixed set of the inverse involution on Lie groups, building on prior results about centralizers.
Findings
Provides a general calculation method for fixed sets of inverse involution.
Extends previous work on centralizer isomorphism types.
Offers explicit procedures applicable to various Lie groups.
Abstract
In [H. Duan and S. Liu, The isomorphism type of the centralizer of an element in a Lie group, Journal of algebra, 376(2013), 25-45], we have determined the isomorphism type of the centralizer of an element in a simpe Lie group. As a sequel to [H. Duan and S. Liu, The isomorphism type of the centralizer of an element in a Lie group, Journal of algebra, 376(2013), 25-45.] we present a general procedure to calculate the isomorphism type of the fixed set of the inverse involution on a Lie group.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Topics in Algebra · Advanced Algebra and Geometry