单项代数的表示具有多指数复杂度
Representations of monomial algebras have poly-exponential complexities
摘要：
我们使用有向图称为“合之箭图”来研究有限维代数的合之表示的维数的渐近增长率。对于单项式代数的任意一个生成的表示，证明了这个增长率是多指数的，即多项式和指数函数的乘积，并给出了由合冲代数计算相应的次数和基的方法.我们的特征的增长率在这种情况下产生的：发生的指数函数的基础是真正的，非负的代数整数$b$的不可约多项式超过$\mathbb{Q}$没有根与大于$b$的模。此外，我们表明，这些增长率是稳定的派生等价不变。
英文摘要：
We use directed graphs called "syzygy quivers" to study the asymptotic growth rates of the dimensions of the syzygies of representations of finite dimensional algebras. For any finitely generated representation of a monomial algebra, we show that this growth rate is poly-exponential, i.e. the product of a polynomial and an exponential function, and give a procedure for computing the corresponding degree and base from a syzygy quiver. We characterize the growth rates arising in this context: The bases of the occurring exponential functions are the real, nonnegative algebraic integers $b$ whose irreducible polynomial over $\mathbb{Q}$ has no root with with modulus larger than $b$. Moreover, we show that these growth rates are invariant under stable derived equivalences.
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