逆与对极重合的连通分次代数范畴中的半群
Cogroups in the category of connected graded algebras whose inverse and antipode coincide
摘要：
设A是交换环R上连通分次代数范畴中的余群。设nu表示A的逆，chi表示A的底层霍普夫代数的对极.我们阐明了nu与chi的异同，并证明了nu与chi重合的充要条件是A作为分次代数是交换的.设A^co_CG是满足这些等价条件的上群范畴。如果R是域，则范畴A^co_CG是完全确定的。我们还建立了A^co_CG的有限型对象构成的满子范畴与正分次R-模范畴的一个满子范畴的等价性，而不对R作任何假设.在R=Q的情况下的结果被应用到co-H-群的理论。
英文摘要：
Let A be a cogroup in the category of connected graded algebras over a commutative ring R. Let nu denote the inverse of A and chi the antipode of the underlying Hopf algebra of A. We clarify the differences and similarities of nu and chi, and show that nu coincides with chi if and only if A is commutative as a graded algebra. Let A^co_CG be the category of cogroups satisfying these equivalent conditions. If R is a field, the category A^co_CG is completely determined. We also establish an equivalence of the full subcategory of A^co_CG consisting of objects of finite type with a full subcategory of the category of positively graded R-modules without any assumption on R. The results in the case of R=Q are applied to the theory of co-H-groups.
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