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Onset of Regularity for FI-modules
In terms of local cohomology, we give an explicit range as to when the FI -homology of an FI -module attains the degree predicted by its regularity.
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On w-FI-flat and w-FI-injective modules
In this paper, we generalize, with respect to the w -operation, the notions of FI -injective and FI -flat modules introduced by L. Mao and N. Ding. Let R ...
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On FI-t-lifting modules
In this paper, we introduce the notion of FI-t-lifting modules which is a proper generalization of both the concepts of t-lifting modules and...
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On a Generalization of FI-Extending Modules
In this paper, we introduce modules with the property that every f-closed submodule has a complement which is a direct summand. We provide some...
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Linear stable range for homology of congruence subgroups via FI-modules
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a...
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On the symmetric group action on rigid disks in a strip
In this paper we decompose the rational homology of the ordered configuration space of n open unit-diameter disks in the infinite strip of width 2 as...
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Projection Invariant t-Baer and Related Modules
We study the concepts of projection invariant t -extending modules and projection invariant t -Baer modules, which are generalized to the notions of...
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Finite Dimensional Modules over Indefinite Kac–Moody Lie Algebras
In this paper, we study the finite dimensional modules over indefinite Kac–Moody Lie algebras. We prove that any Kac–Moody Lie algebra with...
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Twisted Whittaker modules over \({U_q}({\mathfrak{g}\mathfrak{l}_{n + 1}})\)
As is well known, the classical nonsingular Whittaker modules over quantum groups cannot be defined for non A 1 -type. In this paper, by choosing...
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A(∞)-Algebra Structure in the Cohomology and Cohomologies of a Free Loop Space
The cohomology algebra of the space H ∗ ( X ) defines neither cohomology modules of the loop space H ∗ (Ω X ) nor cohomologies of the free loop space H ∗ (Λ X ...
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Characteizations of woven g-frames and weaving g-frames in Hilbert spaces and C*-modules
In this paper, using Parseval frames we generalize Sun’s results to g-frames in Hilbert C *-modules. Moreover, for g-frames in Hilbert spaces, we...
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Representation Stability and Finite Orthogonal Groups
In this paper, we prove homological stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and...
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Recollements of Derived Categories from Two-Term Big Tilting Complexes
We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting...
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Birational Maps to Grassmannians, Representations and Poset Polytopes
We study the closure of the graph of the birational map from a projective space to a Grassmannian. We provide explicit description of the graph...
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Module Categories of Small Radical Nilpotency
This paper aims to initiate a study of the representation theory of representation-finite artin algebras in terms of the nilpotency of the radical of...