eBook

Descent in Buildings (AM-190)

Weiss, Richard M, Petersson, Holger P, Mühlherr, Bernhard

2015

Overview

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or \"form\" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a \"residually pseudo-split\" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.

• Publisher: Princeton University Press
• Subject: Addition / Additive group / Affine space / Affine transformation / Algebra & number theory / Algebraic / Algebraic geometry / Algebraic group / Algebraic structure / Algebraically closed field / Automorphism / Bijection / Biquaternion / Buildings (Group theory) / Cardinality / Combinatorial geometry / Combinatorics / Composition algebra / Convex hull / Coset / Coxeter group / Diagram (category theory) / Dimension (vector space) / Discrete valuation / Division algebra / Dynkin diagram / Embedding / Empty set / Equivalence class / Euclidean space / Existential quantification / Field extension / Finite set / Galois group / General Topics for Engineers / Geometry / Half-space (geometry) / Homomorphism / Hyperbolic geometry / Hyperplane / Linear combination / Linear map / Linear space (geometry) / Linear subspace / Local field / Mathematical induction / MATHEMATICS / MATHEMATICS / General / MATHEMATICS / Geometry / General / Metric space / Module (mathematics) / Moufang polygon / Moufang set / Non-abelian / Octonion / Octonion algebra / Permutation / Power set / Projective space / Purely inseparable extension / Quadratic form / Quaternion / Quaternion algebra / Residue field / Root system / Scientific notation / Separable extension / Set (mathematics) / Simplicial complex / Special case / Splitting field / Subgroup / Subring / Subset / Substructure / Summation / Surjective function / Theorem / Unit sphere / Vector space
• ISBN: 9781400874019, 1400874017, 9780691166902, 0691166900, 0691166919, 9780691166919