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Twin trees and $\lambda _{\Lambda }$-gons


Author: Curtis D. Bennett
Journal: Trans. Amer. Math. Soc. 349 (1997), 2069-2084
MSC (1991): Primary 51E12, 20E99
DOI: https://doi.org/10.1090/S0002-9947-97-01703-0
MathSciNet review: 1370635
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Abstract: We define a natural generalization of generalized $n$-gons to the case of $\Lambda $-graphs (where $\Lambda $ is a totally ordered abelian group and $0<\lambda \in \Lambda$). We term these objects $\lambda _{\Lambda }$-gons. We then show that twin trees as defined by Ronan and Tits can be viewed as $(1,0)_{\Lambda }$-gons, where $\Lambda = Z \times Z$ is ordered lexicographically. This allows us to then generalize twin trees to the case of $\Lambda $-trees. Finally, we give a free construction of $\lambda _{\Lambda }$-gons in the cases where $\Lambda $ is discrete and has a subgroup of index $2$ that does not contain the minimal element of $\Lambda $.


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Additional Information

Curtis D. Bennett
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email: cbennet@andy.bgsu.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01703-0
Keywords: $\Lambda$-trees, twin trees, generalized $n$-gons
Received by editor(s): April 24, 1994
Received by editor(s) in revised form: January 4, 1996
Additional Notes: The author gratefully acknowledges the support of an NSF postdoctoral fellowship.
Article copyright: © Copyright 1997 American Mathematical Society

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