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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A reduced Tits quadratic form and tameness of three-partite subamalgams of tiled orders


Author: Daniel Simson
Journal: Trans. Amer. Math. Soc. 352 (2000), 4843-4875
MSC (2000): Primary 16G30, 16G50, 15A21; Secondary 15A63, 16G60
Published electronically: June 8, 2000
MathSciNet review: 1695036
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Abstract:

Let $D$ be a complete discrete valuation domain with the unique maximal ideal ${\mathfrak{p}}$. We suppose that $D$ is an algebra over an algebraically closed field $K $ and $D/{\mathfrak{p}} \cong K$. Subamalgam $D$-suborders $\Lambda ^{\bullet }$ of a tiled $D$-order $\Lambda $ are studied in the paper by means of the integral Tits quadratic form $q_{\Lambda ^{\bullet }}: {\mathbb{Z} }^{n_{1}+2n_{3}+2 } \,\,\longrightarrow {\mathbb{Z} }$. A criterion for a subamalgam $D$-order $\Lambda ^{\bullet }$ to be of tame lattice type is given in terms of the Tits quadratic form $q_{{\Lambda ^{\bullet }}}$ and a forbidden list $\Omega _{1},\ldots ,\Omega _{17}$ of minor $D$-suborders of $\Lambda ^{\bullet }$presented in the tables.


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Additional Information

Daniel Simson
Affiliation: Faculty of Mathematics and Informatics, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland
Email: simson@mat.uni.torun.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02575-7
PII: S 0002-9947(00)02575-7
Received by editor(s): November 12, 1997
Published electronically: June 8, 2000
Additional Notes: Partially supported by Polish KBN Grant 2 P0 3A 012 16.
Dedicated: Dedicated to Klaus Roggenkamp on the occasion of his 60th birthday
Article copyright: © Copyright 2000 American Mathematical Society