Twisted Weyl Groups of Compact Lie Groups and Nonabelian Cohomology

Ming Liu and Xia Zhang
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Ming Liu: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Xia Zhang: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China

Mathematics, 2019, vol. 8, issue 1, 1-10

Abstract: Given a compact connected Lie group G with an S 1 -module structure and a maximal compact torus T of G S 1 , we define twisted Weyl group W ( G , S 1 , T ) of G associated to S 1 -module and show that two elements of T are δ -conjugate if and only if they are in one W ( G , S 1 , T ) -orbit. Based on this, we prove that the natural map W ( G , S 1 , T ) \ H 1 ( S 1 , T ) → H 1 ( S 1 , G ) is bijective, which reduces the calculation for the nonabelian cohomology H 1 ( S 1 , G ) .

Keywords: twisted Weyl groups; compact Lie groups; ? -conjugate; nonabelian cohomology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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