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

Daniel Simson
2000 Transactions of the American Mathematical Society  
Let D be a complete discrete valuation domain with the unique maximal ideal p. We suppose that D is an algebra over an algebraically closed field K and D/p ∼ = K. Subamalgam D-suborders Λ • of a tiled D-order Λ are studied in the paper by means of the integral Tits quadratic form q Λ • : Z n 1 +2n 3 +2 −→ Z. A criterion for a subamalgam D-order Λ • to be of tame lattice type is given in terms of the Tits quadratic form q Λ • and a forbidden list Ω 1 , . . . , Ω 17 of minor D-suborders of Λ • presented in the tables.
doi:10.1090/s0002-9947-00-02575-7 fatcat:buzrrkyh4jgixd5tfi4sjbf264