论文标题
双模型的主要维度方法
A bimodule approach to dominant dimension
论文作者
论文摘要
我们表明，有限的维数代数$ a $具有主要的维度，至少$ n \ geq 2 $，并且仅当常规的bimodule $ a $ a $ as $ n $ n $ -torsionfree当且仅当$ a \ a \ a \ a \ cong cong occonm octom a \ a \ cong occonm octh {n}（\ text {tr} {tr}（tr}（tr}）） $ v = \ text {hom} _a（d（a），a）$是\ cite {fky}的规范$ a $ bimodule。我们将其应用于霍基柴尔德同源性和共同体的新公式，并为代数至少两个，并在第一个tachikawa猜想，nakayama猜想和戈伦斯坦同源代数之间显示出新的关系。
We show that a finite dimensional algebra $A$ has dominant dimension at least $n \geq 2$ if and only if the regular bimodule $A$ is $n$-torsionfree if and only if $A \cong Ω^{n}(\text{Tr}(Ω^{n-2}(V)))$ as $A$-bimodules, where $V=\text{Hom}_A(D(A),A)$ is the canonical $A$-bimodule in the sense of \cite{FKY}. We apply this to give new formulas for the Hochschild homology and cohomology for algebras with dominant dimension at least two and show a new relation between the first Tachikawa conjecture, the Nakayama conjecture and Gorenstein homological algebra.
