共深度2及相关主题
Codepth Two and Related Topics
摘要：
深度为2的扩张$A \| B$在其双中心化子$V_A(V_A(B))$上是弱深度为2的，如果它在$B$上是可分的。我们考虑各种例子和非例子的深度1和2属性。研究了深度2与代数的直积、张量积以及相关Hochschild上链的杯积的关系。第6节引入了余深度2余代数同态$g: C \to D$的概念，它是深度2代数同态的对偶.证明了双余自同态$\End {}^DC^D$的自同态环在对偶代数$C^*$的中心化子代数$g^*: D^* \to C^*$上形成右双代数胚.
英文摘要：
A depth two extension $A \| B$ is shown to be weak depth two over its double centralizer $V_A(V_A(B))$ if this is separable over $B$. We consider various examples and non-examples of depth one and two properties. Depth two and its relationship to direct and tensor product of algebras as well as cup product of relative Hochschild cochains is examined. Section~6 introduces a notion of codepth two coalgebra homomorphism $g: C \to D$, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms $\End {}^DC^D$ forms a right bialgebroid over the centralizer subalgebra $g^*: D^* \to C^*$ of the dual algebra $C^*$.
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