T(2,2,2,2)型tubular代数的合成代数

Composition Algebras of Tubular Algebras of Type T(2,2,2,2)

设A为有限域上的T(2,2,2,2)型tubular代数,它是tame遗传代数A0的单点扩张,也是tame遗传代数A∞的单点余扩张．记P0为预投射A0-模集合,L∞是预内射A∞-模集合,则P0,L∞(?)mod A记T=mod A＼(P0∪L∞)．本文证明A的合成代数C(A)具有形为P0·J·L∞的三角分解．

Let A be a tubular algebra of type T（2, 2, 2, 2） over a finite field κ. It is the one-point extension of a tame hereditary algebra A0 and also the one-point coextension of a tame hereditary algebra A∞. Let P0 be the set of preprojective A0-modules and -L∞ be the set of preinjective A∞-modules. Then we have P0, L∞ belong to mod A. We denote T=mod A／（P0 U L∞）. In this paper, we get a triangular decomposition structure P0·F·L∞ for the composition algebra C.（A） of A.