Galois Involutions
This chapter focuses on the fixed points of a strictly semi-linear automorphism of order 2 of a spherical building which satisfies the conditions laid out in Hypothesis 30.1. It begins with the fhe definition of a spherical building satisfying the Moufang condition and a Galois involution of Δ, des...
| Main Authors: | , , |
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| Format: | Book |
| Language: | unknown |
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Princeton University Press
2017
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.23943/princeton/9780691166902.003.0031 |
| Summary: | This chapter focuses on the fixed points of a strictly semi-linear automorphism of order 2 of a spherical building which satisfies the conditions laid out in Hypothesis 30.1. It begins with the fhe definition of a spherical building satisfying the Moufang condition and a Galois involution of Δ, described as an automorphism of Δ of order 2 that is strictly semi-linear. It can be recalled that Δ can have a non-type-preserving semi-linear automorphism only if its Coxeter diagram is simply laced. The chapter assumes that the building Δ being discussed is as in 30.1 and that τ is a Galois involution of Δ. It also considers the notation stating that the polar region of a root α of Δ is the unique residue of Δ containing the arctic region of α. |
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