Affine $\Lambda$-Buildings II

TL;DR

This paper simplifies the axiomatic framework of affine bb-Lambda buildings by extending Euclidean building axioms and introducing a strong exchange condition involving apartments and sectors.

Contribution

It provides a more accessible set of axioms for affine bb-Lambda buildings, building on and extending prior Euclidean building results.

Findings

Simplified axioms for affine bb-Lambda buildings

Extension of Parreau's Euclidean building axioms

Introduction of a strong exchange condition

Abstract

The purpose of this paper is to provide an easier set of axioms for Affine $\Lambda$-Buildings by extending results of Anne Parreau on the equivalence of axioms for Euclidean buildings. In particular we give an easier set of axioms for an affine $\Lambda$-building, utilizing a notion of a strong exchange condition on apartments and sectors having a sector panel lying in an apartment.