$A_n-$型有限维代数的整体维数

On Global Dimensions of $A_n$-Type Finite Dimensional Algebras

中文关键词:  整体维数  有限维代数  箭图  容许理想

英文关键词:global dimension  finite dimensional $k$-algebra  quiver  admissible ideal

中文摘要:

      设$k$是一个代数闭域, $n$是一个自然数,本文给出了一个精确刻画$A_{n}$-型有限维$k$-代数的整体维数的技巧.据此给出了$A_{n}$-型有限维$k$-代数的所有可能的整体维数.特别的,如果$n>1$,我们指出其中最大的是 $n-1$,最小的是 $1$.

英文摘要:

      A technique is provided to explicitly describe global dimensions of all $A_{n}$-type finite dimensional $k$-algebras for $k$ an algebraic closed field. All possible global dimensions of all $A_n$-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is $n-1$, and the minimum is $1$ for $n>1$.