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ρ0为预投射A0-模集合,L∞是预内射A∞-模集合,则ρ0,L∞ belong to mod A.记T=mod A\(P0 U L∞).本文证明A的合成代数C(A)具有形为ρ0·F·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.