自由扩张与Jordan型
Free Extensions and Jordan type
摘要：
T. Harima和J. Watanabe。由Artin代数的幂零元乘的乘法映射$m$的Jordan型是确定$m$的Jordan矩阵中的块的大小的划分。证明了具有纤维$B$的Artin代数$A$的自由扩张是通常的张量积的变形.这对$A,B$和$C$的通用Jordan型有影响，表明$C$的Jordan型至少是优势阶中通常的张量积的Jordan型。给出了多项式环上线性群作用的相对余不变量在代数中的应用。
英文摘要：
Free extensions of commutative Artinian algebras were introduced by T. Harima and J. Watanabe. The Jordan type of a multiplication map $m$ by a nilpotent element of an Artinian algebra is the partition determining the sizes of the blocks in a Jordan matrix for $m$. We show that a free extension of the Artinian algebra $A$ with fibre $B$ is a deformation of the usual tensor product. This has consequences for the generic Jordan types of $A,B$ and $C$, showing that the Jordan type of $C$ is at least that of the usual tensor product in the dominance order. We give applications to algebras of relative coinvariants of linear group actions on a polynomial ring.
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