论文标题
偏斜式代数和Orbifolds的派生类别
Derived categories of skew-gentle algebras and orbifolds
论文作者
论文摘要
偏斜的代数是对它们具有许多共同特性的众所周知的柔和代数类别的概括。在这项工作中，使用非共同的Gröbner基础理论，我们表明这些代数是Koszul，并且Koszul Dual再次偏斜。我们根据Orbifold表面的多边形解剖来给出其有限的衍生类别的几何模型，该模型在Orbifold和不可传代的对象中建立了曲线之间的对应关系。此外，我们表明Orbifold解剖编码偏斜式代数的同源性特性，例如它们的奇异性类别，其Gorenstein尺寸和衍生的不变性，例如其Q-Cartan矩阵的决定因素。
Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gröbner basis theory, we show that these algebras are Koszul and that the Koszul dual is again skew-gentle. We give a geometric model of their bounded derived categories in terms of polygonal dissections of orbifold surfaces establishing a correspondence between curves in the orbifold and indecomposable objects. Moreover, we show that the orbifold dissections encode homological properties of skew-gentle algebras such as their singularity categories, their Gorenstein dimensions and derived invariants such as the determinant of their q-Cartan matrices.
