Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.02977

Filtrations and Homological degrees of FI-modules

Liping Li·Nina Yu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let $k$ be a commutative Noetherian ring. In this paper we consider filtered modules of the category FI firstly introduced by Nagpal. We show that a finitely generated FI-module $V$ is filtered if and only if its higher homologies all vanish, and if and only if a certain homology vanishes. Using this homological characterization, we characterize finitely generated FI-modules $V$ whose projective dimension is finite, and describe an upper bound for it. Furthermore, we give a new proof for the fact that $V$ induces a finite complex of filtered modules, and use it as well as a result of Church and Ellenberg to obtain another upper bound for homological degrees of $V$.

Explore related subjects

math.RTmath.KTmath.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Liping Li, Nina Yu. 2016-11-14. Filtrations and Homological degrees of FI-modules. https://arxiv.org/abs/1511.02977

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Course on Lie algebras and Chevalley groups

These are expanded notes from graduate courses about Lie algebras and Chevalley groups held at the University of Stuttgart. In the 1950s Chevalley showed how linear groups over arbitrary fields could be obtained~ -- ~by a uniform procedure~ -- ~from the simple Lie algebras over $\C$ occurring in the Cartan--Killing classification. Together with subsequent variations, Chevalley's work had a profound and long-lasting impact on group theory and Lie theory in general. Classical, and widely used references are the lectures notes by Steinberg (1967) and the monograph by Carter (1972). Our aim here is to present a self-contained introduction to the theory of Chevalley groups, based on recent simplifications arising from Lusztig's fundamental theory of ``canonical bases''. A further feature of our text is that we explicitly incorporate algorithmic methods in our treatment, both for the handling of substantial examples and regarding some aspects of the general theory. Eventually, this may turn into a book project.

math.RT↗
arXiv2026

On the p-part of the conductor of a generalised character

We show that the $p$-part of the conductor of a generalised character of a finite group is equal to the conductor of its generalised decomposition numbers. We use this to show that $p$-parts of conductors of irreducible characters are preserved under isotypies and perfect isometries that arise in the context of stable equivalences of Morita type with endopermutation source. We apply this to blocks with abelian defect and Frobenius inertial quotient.

math.RT↗
arXiv2026

On the triviality of inhomogeneous deformations of $\mathfrak{osp}(1|2n)$

We specify a symmetrized mixed-oscillator deformation family of $B(0,n)=\operatorname{osp}(1|2n)$, with even mixed coefficients and one odd square-zero parameter. For every $n\geq1$, we derive its bracket from a faithful oscillator realization and exhibit an odd cochain whose coboundary is the recovered deformation coefficient. The resulting even change of generators is an exact isomorphism over the exterior parameter algebra. For $n=1$, the cochain agrees with the normalization of Bakalov-Sullivan. We give the source relations and the even-central specialization explicitly, together with a Lean 4 formalization.

math.RT↗