Classification of the Absolute-Valued Algebras with Left-Unit Satisfying x2(x2)2 = (x2)2x2

On finite-dimensional absolute-valued algebras satisfying (x^p,x^q,x^r)=0

By means of principal isotopes lH(a,b) of the algebra lH [Ra 99] we give an exhaustive and not repetitive description of all 4-dimensional absolute-valued algebras satisfying (x^p, x^q, x^r) = 0 for fixed integers p, q, r \in\{1,2\}. For such an algebras the number N(p,q,r) of isomorphism classes is 2 or 3, or is infinite. Concretely 1. N(1,1,1)=N(1,1,2)=N(1,2,1)=N(2,1,1)=2, 2. N(1,2,2)=N(2,2,1)=3, 3. N(2,1,2)=N(2,2,2)=\infty. Besides, each one of the above algebras contains 2-dimensional subalgebras. However, the problem in dimension 8 is far from being completely solved. In fact, there are 8…

关于非单缀丛代数的一种方法

An approach to non simply laced cluster algebras

设$Δ$是一个有向值图，它具有一组满足一定稳定性条件的容许自同构.证明了与值商图$Δ/G$相关联的（无系数）簇代数$\mathcal A(Δ/G)$是通过$G$的作用与$Δ$相关联的簇代数的商$π(\mathcal A(Δ))$的子代数.当$Δ$是Dynkin图时，证明了$\mathcal A(Δ/G)$与$π(\mathcal A(Δ))$重合.作为应用的一个例子，我们证明了仿射值图是突变有限的，给出了Seven的一个结果的另一种证明。