Leseprobe
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Descent in Buildings (AM-190)
Bernhard Mühlherr, Richard M. Weiss, Holger P. Petersson, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Moufang polygon, Surjective function, Affine space, Cardinality, Linear space (geometry), Coset, Existential quantification, Special case, Dimension (vector space), Half-space (geometry), Mathematical induction, Non-abelian, Quaternion algebra, Residue field, Linear subspace, Octonion, Finite set, Permutation, Algebraic geometry, Algebraic structure, Linear combination, Euclidean space, Separable extension, Quadratic form, Moufang set, Subring, Algebraic group, Embedding, Additive group, Diagram (category theory), Galois group, Composition algebra, Empty set, Subset, Algebraically closed field, Splitting field, Root system, Automorphism, Convex hull, Local field, Power set, Hyperbolic geometry, Unit sphere, Field extension, Purely inseparable extension, Dynkin diagram, Hyperplane, Linear map, Affine transformation, Discrete valuation, Projective space, Addition, Subgroup, Division algebra, Equivalence class, Biquaternion, Theorem, Coxeter group, Simplicial complex, Homomorphism, Metric space, Vector space, Scientific notation, Set (mathematics), Bijection, Module (mathematics), Quaternion, Summation, Octonion algebra, Substructure