论文标题
双重交叉产品扩展的最小深度
Minimum depth of double cross product extensions
论文作者
论文摘要
在本文中，我们探讨了有限尺寸HOPF代数的双交叉产品的最小奇数和最小深度子代数对。我们首先定义分解代数，并概述在这种情况下的下属深度与给定子代数的常规左模块表示的模块深度有关。接下来，我们研究双重跨产品HOPF亚类的最小奇数深度，并根据其相关模块的深度确定其价值，我们得出结论，Drinfeld Double Hopf subgebras的最小奇数深度为3。最终，我们在双跨产品Hopf Subergebra扩展中产生了深度2的必要条件。然后使用这种足够的条件来证明Drinfeld Double Hopf子代理中最小深度2的结果，尤其是在有限的HOPF代数的情况下。最后，我们在双重交叉产品方案中为普通HOPF子代理的中心设备提供公式。
In this paper we explore minimum odd and minimum even depth sub algebra pairs in the context of double cross products of finite dimensional Hopf algebras. We start by defining factorization algebras and outline how subring depth in this context relates with the module depth of the regular left module representation of the given subalgebra. Next we study minimum odd depth for double cross product Hopf subalgebras and determine their value in terms of their related module depth, we conclude that minimum odd depth of Drinfeld double Hopf subalgebras is 3. Finaly we produce a necessary and sufficient condition for depth 2 in double cross product Hopf subalgebra extensions. This sufficient condition is then used to prove results regarding minimum depth 2 in Drinfeld double Hopf subalgebras, particularly in the case of finite Group Hopf algebras. Lastly we provide formulas for the centralizer of a normal Hopf subalgebra in a double cross product scenario.
