Abstract
n-recollements of triangulated categories and n-derived-simple algebras are introduced. The relations between the n-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry conjecture is reduced to 2-derived-simple algebras.
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Presented by Claus Michael Ringel.
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Qin, Y., Han, Y. Reducing Homological Conjectures by n-Recollements. Algebr Represent Theor 19, 377–395 (2016). https://doi.org/10.1007/s10468-015-9578-z
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DOI: https://doi.org/10.1007/s10468-015-9578-z
Keywords
- n-recollement
- n-derived-simple algebra
- Cartan determinant
- Homologically smooth algebra
- Gorenstein algebra