论文标题
塞雷函子的熵，用于较高的世袭代数
Entropies of Serre functors for higher hereditary algebras
论文作者
论文摘要
对于较高的遗传代数，我们计算其上部（下）serre尺寸，serre函数的熵和多项式熵以及serre Quasi函数的Hochschild（CO）同源性熵。这些不变性由其Calabi-yau维度给出，以实现更高的表示代数，其全局尺寸以及其Coxeter矩阵的光谱半径和多项式生长速率，用于较高的表示限制代数。为此，我们证明了有限的全球维度的有限维度基本代数的Hochschild同源性熵的Yomdin类型不平等。 Our calculations imply that the Kikuta and Ouchi's question on relations between entropy and Hochschild (co)homology entropy has positive answer, and the Gromov-Yomdin type equalities on entropy and Hochschild (co)homology entropy hold, for the Serre functor on perfect derived category and the Serre quasi-functor on perfect dg module category of an indecomposable elementary higher hereditary algebra.
For a higher hereditary algebra, we calculate its upper (lower) Serre dimension, the entropy and polynomial entropy of Serre functor, and the Hochschild (co)homology entropy of Serre quasi-functor. These invariants are given by its Calabi-Yau dimension for a higher representation-finite algebra, and by its global dimension and the spectral radius and polynomial growth rate of its Coxeter matrix for a higher representation-infinite algebra. For this, we prove the Yomdin type inequality on Hochschild homology entropy for a finite dimensional elementary algebra of finite global dimension. Our calculations imply that the Kikuta and Ouchi's question on relations between entropy and Hochschild (co)homology entropy has positive answer, and the Gromov-Yomdin type equalities on entropy and Hochschild (co)homology entropy hold, for the Serre functor on perfect derived category and the Serre quasi-functor on perfect dg module category of an indecomposable elementary higher hereditary algebra.
