The Grothendieck group of an n-angulated category
The Grothendieck group of an n-angulated category
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DOI：
10.1016/j.jpaa.2013.06.007
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
P. A. Bergh;Marius Thaule
中科院分区：
文献类型：
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作者：
P. A. Bergh;Marius Thaule
我们定义了一个n-角范畴的Grothendieck群，并证明了对于奇数n，它的性质与n= 3的特殊情况相同，即三角化的情况。特别地，它的子群通过双射对应对稠密和完备的n-角化子范畴进行分类。对于一个张量n-角化范畴，Grothendieck群成为一个环，其理想分类了范畴的稠密和完备的n-角化张量理想。
We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n= 3, ie the triangulated case. In particular, its subgroups classify the dense and complete n-angulated subcategories via a bijective correspondence. For a tensor n-angulated category, the Grothendieck group becomes a ring, whose ideals classify the dense and complete n-angulated tensor ideals of the category.