Backström algebras. (English) Zbl 1527.16010
Backstrom pairs and Backstrom rings are presented, their derived categories are explored, and a form of categorical resolution is built for them in this study. Additionally, the global dimension is established, a semiorthogonal decomposition of the derived category is created, and it is concluded that a Backstrom ring’s derived dimension could only be two at most. The authors define the derived category as the category of components of a certain bimodule using this semiorthogonal decomposition. The global dimension of the latter is established by creating a partial tilting for a Backstrom pair to a ring of triangular matrices.
Reviewer: Udhayakumar Ramalingam (Vellore)
MSC:
| 16E35 | Derived categories and associative algebras |
| 16E10 | Homological dimension in associative algebras |
| 18G80 | Derived categories, triangulated categories |
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