2010/11/16 by Tom Howard, Howard, Tom · 1 citation
Mathematics · #16D90 #16E05 #16E35 #16G10 #16G20 #16P10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D90 #msc:16E05 #msc:16E35 #msc:16G10 #msc:16G20 #msc:16P10
paper · pdf · doi:10.48550/arxiv.1011.3554
openalex publication_date 2010/11/16 · arxiv created 2010/11/20 · arxiv updated 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℚ has no root with with modulus larger than b. Moreover, we show that these growth rates are invariant under stable derived equivalences.