Constructions when Φ has a double bond
Constructions when Φ has a double bond
This chapter describes constructions when Φ has a double bond. In particular, it considers a construction that goes beyond SO(q)'s and provides the right generalization of the basic exotic construction for type-Bn when n is not equal to 2. A type-B generalized basic exotic k-group is the universal smooth k-tame central extension of a type-B adjoint generalized basic exotic k-group. The root-field hypothesis in the rank-1 adjoint type-B case is automatic in the higher-rank case. The chapter also builds a large class of absolutely pseudo-simple k-groups of type C via fiber products using type-B generalized basic exotic groups. Finally, it discusses exceptional construction for rank-2 and introduces auxiliary Weil restrictions to explain how the generalized exotic groups of types B and C, as well as the rank-2 basic exceptional groups, underlie a construction beyond the standard case that is exhaustive under a locally of minimal type hypothesis.
Keywords: double bond, exotic construction, k-tame central extension, rank-1, generalized exotic group, rank-2, Weil restriction, minimal type, pseudo-simple k-group
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