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Let $mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors $mod$-$mathcal{M}$ modulo the subcategory of effaceable functors $mod_0$-$mathcal{M}$ has an $n$-cluster tilting subcategory which is equivalent to $mathcal{M}$. This gives a higher-dimensional version of Auslanders formula.
Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact categories and $(n
The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category $operatorname{mod_{mathsf{adm}}}(mathcal{E})$ of admissibly finitely presented functors and use it to give a version of Auslander
We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of simple modules similar to the Weyl-Kac character formula. For the remaini
In 1980, Lusztig introduced the periodic Kazhdan-Lusztig polynomials, which are conjectured to have important information about the characters of irreducible modules of a reductive group over a field of positive characteristic, and also about those o
Let $SsubsetPs^r$ ($rgeq 5$) be a nondegenerate, irreducible, smooth, complex, projective surface of degree $d$. Let $delta_S$ be the number of double points of a general projection of $S$ to $Ps^4$. In the present paper we prove that $ delta_Sleq{bi