关于可分代数的Maschke定理

Maschke's Theorem of Separable Algebra

给出如下几个主要结论：①设Ａ为可分代数，则Ｃ余可分当且仅当卷积余代数ＡＣ余可分；②设Ａ为有限维半单可换Ｈｏｐｆ代数，Ｂ为Ａ的子Ｈｏｐｆ代数，如果Ａ余可分，那么Ｓｍａｓｈ积＃（Ａ，Ｂ）为可分代数；③设Ｋ→ｆＨｇπＬ，为Ｈｏｐｆ代数的可裂短正合序列，则Ｈ余可分当且仅当Ｋ，Ｌ余可分，且当Ｈ双可分时。

This paper primarily gives the following conclusions: ① Let A be an algebra, thus C is a coseparable coalgebra if and only if A*C is a coseparable convolution coalgebra; ② Let A be a dimensional semisimple commutative Hopf algebra and B be a sub Hopf algebra of A . if A is a coseparable coalgebra, then smash product #(A,B) is a separable algebra; ③ Let K[DD(]fHgπL be a split short exact sequence of Hopf algebras, thus H is a coseparable Hopf algebra if and only if K and L are coseparable Hopf algebras, also if H is a bi separable Hopf algebra, then L is a bi separable Hopf algebra.