Upper bounds of homological invariants of $FI_G$-modules

Liping Li

Upper bounds of homological invariants of $FI_G$-modules

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arxiv 1512.05879 v3 pith:7EWFTWIZ submitted 2015-12-18 math.RT math.KTmath.RA

Liping Li This is my paper · ORCID

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abstract

In this paper we use a homological approach to obtain upper bounds for a few homological invariants of $FI_G$-modules $V$. These upper bounds are expressed in terms of the generating degree and torsion degree, which measure the top and socle of $V$ under actions of non-invertible morphisms in the category respectively.

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An inductive method for $\mathrm{OI}$-modules
math.RT 2019-09 accept novelty 7.0 of 10

An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.

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