On the global dimension of the endomorphism algebra of a τ-tilting module

2021 ◽  
Vol 225 (11) ◽  
pp. 106740
Author(s):  
Pamela Suarez
2013 ◽  
Vol 20 (03) ◽  
pp. 443-456
Author(s):  
Jingjing Guo

Let A be a hereditary Artin algebra and T a tilting A-module. The possibilities for the global dimension of the endomorphism algebra of a generator-cogenerator for the subcategory T⊥ in A-mod are determined in terms of relative Auslander-Reiten orbits of indecomposable A-modules in T⊥.


2020 ◽  
pp. 1-27
Author(s):  
MATTHEW PRESSLAND ◽  
JULIA SAUTER

Abstract We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting properties, for example, that their endomorphism algebras always have global dimension less than or equal to that of the original algebra. We characterise minimal d-Auslander–Gorenstein algebras and d-Auslander algebras via the property that these special tilting and cotilting modules coincide. By the Morita–Tachikawa correspondence, any algebra of dominant dimension at least 2 may be expressed (essentially uniquely) as the endomorphism algebra of a generator-cogenerator for another algebra, and we also study our special tilting and cotilting modules from this point of view, via the theory of recollements and intermediate extension functors.


2016 ◽  
Vol 26 (08) ◽  
pp. 1597-1615 ◽  
Author(s):  
Driss Bennis ◽  
J. R. García Rozas ◽  
Luis Oyonarte

We study the relative Gorenstein projective global dimension of a ring with respect to a weakly Wakamatsu tilting module [Formula: see text]. We prove that this relative global dimension is finite if and only if the injective dimension of every module in Add[Formula: see text] and the [Formula: see text]-projective dimension of every injective module are both finite (indeed these three dimensions have a common upper bound). When RC satisfies some extra conditions we prove that the relative Gorenstein projective global dimension of [Formula: see text] is always bounded above by the [Formula: see text]-projective global dimension of [Formula: see text], these two dimensions being equal when the class of all [Formula: see text]-Gorenstein projective [Formula: see text]-modules is contained in the Bass class of [Formula: see text] relative to [Formula: see text]. Of course we also give the dual results concerning the relative Gorenstein injective global dimension.


2015 ◽  
Vol 27 (3) ◽  
Author(s):  
Hongxing Chen ◽  
Changchang Xi

AbstractIn this paper, we consider the endomorphism algebra of an infinitely generated tilting module of the form


Author(s):  
Larysa Nosach ◽  
◽  
Victoria Morgun ◽  

The author's research of the current state and features of the development of the world market for services in conditions of turbulence of world processes was carried; the world leaders of the service sector in the global dimension and leaders of the most dynamic articles of service categories were identified; the share of world exports of services by countries by the level of their economic development was justified; weaknesses in the assessment of indicators of international trade in services were identified; the research is based on UNCTAD statistics.


2021 ◽  
Vol 1 (1) ◽  
pp. 115-133
Author(s):  
Markus Nornes

Abstract This essay examines a regional, not global, dimension of Chinese cinema: the Chinese character in its brushed form. Calligraphy and cinema have an intimate relationship in East Asia. Indeed, the ubiquity of the brushed word in cinema is one element that actually ties works in Korean, Japanese and Sinophone Asia together as a regional cinema. At the same time, I will explore the very specific difference of Chinese filmmakers’ use of written language. On first glance, cinema and calligraphy would appear as radically different art forms. On second glance, they present themselves as sister arts. Both are art forms built from records of the human body moving in (an absent) time and space. The essay ends with a consideration of subtitling, upon which Chinese cinema’s global dimension is predicated. How does investigating this very problem lead us to rethinking the nature of the cinematic subtitle, which is very much alive―a truly movable type?


Religions ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 475
Author(s):  
Francisco Javier Ramón Solans

The objective of this article is to analyse Mexican national pilgrimages to Rome that took place during the pontificate of Leo XIII (1878–1903). These pilgrimages occurred in the context of a global Catholic mobilisation in support of the papacy, during the so-called Roman Question. This paper’s analysis of these pilgrimages draws from historiography about national pilgrimages, as well as studies on Catholic mobilisation in support of the pope in the second half of the nineteenth century. It is fundamentally based on primary sources of an official nature, such as reports and other printed documents produced on the occasion of the pilgrimage. The study’s primary conclusion is that national pilgrimages to Rome had a polysemic character since they brought together various religious and national identities. The pilgrimages contributed simultaneously to reinforcing the link between Catholicism and Mexican national identity and the global dimension of Catholicism and allegiance to the Holy See.


2021 ◽  
pp. 014920632199121
Author(s):  
Ruth V. Aguilera ◽  
J. Alberto Aragón-Correa ◽  
Valentina Marano ◽  
Peter A. Tashman

As corporations’ environmental impact comes under greater scrutiny by global financial, regulatory, and societal stakeholders, management scholars have increasingly focused on the role of corporate governance as a tool for driving environmental initiatives. Still, we lack a comprehensive and systematic understanding of this emergent body of inquiry and a holistic agenda for future research. To address this gap, our integrative framework relates the key corporate governance actors to environmental sustainability outcomes from the extant literature and highlights its main methodological approaches and theoretical arguments. Our framework provides a critical analysis of what we know and points to the knowledge gaps around owners, boards of directors, CEOs, top management teams, and employees as corporate governance actors. We then highlight limitations in the existing literature as significant opportunities for further research to resolve its ambiguous conceptualizations of environmental sustainability constructs, various methodological and theoretical challenges, incomplete engagement with the global dimension of environmental sustainability, and limited analysis of how corporate governance actors may interact to shape environmental sustainability outcomes. We conclude by proposing novel approaches for addressing these issues, which we believe could generate a better way forward on studying the corporate governance of environmental sustainability.


Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).


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