Representation dimension via tilting theory

AbstractLet A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

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Maximal representation dimension of finitep-groups

Journal of Group Theory ◽

10.1515/jgt.2011.071 ◽

2011 ◽

pp. ---

Author(s):

Shane Cernele ◽

Masoud Kamgarpour ◽

Zinovy Reichstein

Keyword(s):

Representation Dimension ◽

Maximal Representation

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KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788710001497 ◽

2010 ◽

Vol 89 (1) ◽

pp. 23-49 ◽

Cited By ~ 9

Author(s):

VOLODYMYR MAZORCHUK

Keyword(s):

Complete Picture ◽

Projective Modules ◽

Koszul Duality ◽

Tilting Theory

AbstractWe give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.

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n-T-COTORSION-FREE MODULES

Glasgow Mathematical Journal ◽

10.1017/s0017089519000107 ◽

2019 ◽

Vol 62 (2) ◽

pp. 297-311

Author(s):

DAJUN LIU ◽

JIAQUN WEI

Keyword(s):

Tilting Modules ◽

Tilting Theory ◽

Free Modules

AbstractIn order to better unify the tilting theory and the Auslander–Reiten theory, Xi introduced a general transpose called the relative transpose. Originating from this, we introduce and study the cotranspose of modules with respect to a left A-module T called n-T-cotorsion-free modules. Also, we give many properties and characteristics of n-T-cotorsion-free modules under the help of semi-Wakamatsu-tilting modules AT.

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Diversity recognition and minority representation in Central and Southeast Europe: a comparative analysis

Nationalities Papers ◽

10.1080/00905992.2014.916660 ◽

2014 ◽

Vol 42 (3) ◽

pp. 426-448 ◽

Cited By ~ 9

Author(s):

István Gergőo Székely ◽

István Horváth

Keyword(s):

Comparative Analysis ◽

Political Representation ◽

Strong Relationship ◽

Legal Analysis ◽

Southeast Europe ◽

Minority Representation ◽

Representation Dimension ◽

General Attitude ◽

External Pressures ◽

Ethnocultural Diversity

The need to handle ethnocultural diversity and the external pressures of Euro-Atlantic integration have led to the development of complex minority rights regimes in Central and Southeast European states. The aim of this paper is to perform a comparative analysis of the political representation dimension of these regimes, and to investigate how the regulations in this domain are related to the more general attitude of states toward diversity recognition and registration. For this purpose, we classify the states according to a series of variables concerning the manner in which ethnocultural diversity is recognized and portrayed, as well as the regulations concerning the representation of minorities, and identify patterns of their incidence. The formal-legal analysis of the constitutions, minority protection laws and of the electoral legislation of the included countries reveals a clear connection between the general attitude of the state toward diversity and the incidence of autonomies, and a less unequivocal, yet strong relationship in the case of minority representation in the national polity.

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