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Related papers: On mutation of {\tau}-tilting modules

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Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra {\Lambda}, we give bijections between two-term tilting complexes in Kb(proj {\Lambda}),…

Representation Theory · Mathematics 2013-12-04 Yuya Mizuno

Let $\tilde{G}$ be a finite group and $G$ a normal subgroup of $\tilde{G}$. In this paper, we give a necessary and sufficient condition for $\mathrm{Ind}_G^{\tilde{G}}M$ to be a support $\tau$-tilting $k\tilde{G}$-module for a $kG$-module…

Representation Theory · Mathematics 2023-02-17 Ryotaro Koshio , Yuta Kozakai

We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…

Representation Theory · Mathematics 2014-05-13 Lidia Angeleri Hügel , Frederik Marks , Jorge Vitória

The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…

Algebraic Geometry · Mathematics 2007-05-23 V. P. Palamodov

In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual…

Algebraic Geometry · Mathematics 2016-08-29 Manuel Blickle , Axel Stäbler

In studying the structure of derived categories of module categories of group algebras or their blocks, it is fundamental to classify support $\tau$-tilting modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting…

Representation Theory · Mathematics 2023-11-29 Naoya Hiramae

Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…

Representation Theory · Mathematics 2020-12-08 Yingying Zhang

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…

Metric Geometry · Mathematics 2008-03-11 D. Frettlöh , B. Sing

We consider the conversion problem for multimodal type theory (MTT) by characterizing the normal forms of the type theory and proving normalization. Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability…

Logic in Computer Science · Computer Science 2021-06-04 Daniel Gratzer

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notion of morphic modules over a commutative ring.

Commutative Algebra · Mathematics 2025-01-20 Faranak Farshadifar

We introduce the notion of AIR tilting subcategories of extended hearts of $t$-structures on a triangulated category associated with silting subcategories. This notion generalizes $\tau_{[d]}$-tilting pairs of extended finitely generated…

Representation Theory · Mathematics 2026-01-29 Jiaqun Wei , Yu Zhou

In this short note, we argue that directed homotopy can be given the structure of generalized modules, over particular monoids. This is part of a general attempt for refoundation of directed topology.

Algebraic Topology · Mathematics 2025-04-21 Eric Goubault

The aim of this work is to clarify the relationship between homology theory of commutative monoids constructed 'a la Quillen and technology of Gamma-modules.

K-Theory and Homology · Mathematics 2014-07-30 R. Kurdiani , T. Pirashvili

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules…

Representation Theory · Mathematics 2015-06-26 Osamu Iyama , Yuji Yoshino

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct…

Representation Theory · Mathematics 2015-08-11 Takahide Adachi

Let $\tilde{G}$ be a finite group, $G$ a normal subgroup of $\tilde{G}$ and $k$ an algebraically closed field of characteristic $p>0$. The first main result in this paper is to show that support $\tau$-tilting $k\tilde{G}$-modules…

Representation Theory · Mathematics 2023-01-13 Ryotaro Koshio , Yuta Kozakai

Given a non-unit, non-zero-divisor, central element $x$ of a ring $\Lambda$, it is well known that many properties or invariants of $\Lambda$ determine, and are determined by, those of $\Lambda / x \Lambda$ and $\Lambda_x$. In the present…

Representation Theory · Mathematics 2018-10-16 Pooyan Moradifar , Shahab Rajabi , Siamak Yassemi

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…

Category Theory · Mathematics 2025-08-28 Paolo Bertozzini , Roberto Conti , Chatchai Puttirungroj

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

Operator Algebras · Mathematics 2007-05-23 David E Evans , Paulo R Pinto

We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $\tau$-tilting pair of $B$-modules is a support…

Representation Theory · Mathematics 2022-11-17 Simion Breaz , Andrei Marcus , George Ciprian Modoi