Triangular matrix coalgebras: Representation theory and recollement

2021 ◽  
Author(s):  
Xuerong Fu ◽  
Hailou Yao ◽  
Yonggang Hu
Keyword(s):  
Representation Theory ◽  
Triangular Matrix

For any triangular matrix coalgebra [Formula: see text], in this paper, we first examine some connections between coalgebra properties of [Formula: see text] and its constituent coalgebras [Formula: see text], [Formula: see text], which contain semiperfectness, computability and row/column-finiteness of their left Cartan matices. Then we devote to considering the coresolution dimensions of recollement of comodule categories by investigating covariantly finite subcategories.

scholarly journals From subcategories to the entire module categories

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Rasool Hafezi
Keyword(s):  
Representation Theory ◽  
Triangular Matrix ◽  
Projective Modules ◽  
Artin Algebra ◽  
Finite Representation ◽  
Triangular Matrix Algebra ◽  
Gorenstein Projective Modules ◽  
Category Of Modules ◽  
Almost Split Sequences ◽  
Auslander Algebra

AbstractIn this paper we show that how the representation theory of subcategories (of the category of modules over an Artin algebra) can be connected to the representation theory of all modules over some algebra. The subcategories dealing with are some certain subcategories of the morphism categories (including submodule categories studied recently by Ringel and Schmidmeier) and of the Gorenstein projective modules over (relative) stable Auslander algebras. These two kinds of subcategories, as will be seen, are closely related to each other. To make such a connection, we will define a functor from each type of the subcategories to the category of modules over some Artin algebra. It is shown that to compute the almost split sequences in the subcategories it is enough to do the computation with help of the corresponding functors in the category of modules over some Artin algebra which is known and easier to work. Then as an application the most part of Auslander–Reiten quiver of the subcategories is obtained only by the Auslander–Reiten quiver of an appropriate algebra and next adding the remaining vertices and arrows in an obvious way. As a special case, when Λ is a Gorenstein Artin algebra of finite representation type, then the subcategories of Gorenstein projective modules over the {2\times 2} lower triangular matrix algebra over Λ and the stable Auslander algebra of Λ can be estimated by the category of modules over the stable Cohen–Macaulay Auslander algebra of Λ.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

A Diferença e a Geografia: O ardil da identidade e a representação da diferença na geografia

GEOgraphia ◽  
2009 ◽  
Vol 1 (1) ◽  
pp. 41
Author(s):  
Ruy Moreira
Keyword(s):  
Representation Theory ◽  
The Difference

Resumo A centração no discurso da identidade fez da geografia um dos campos de saber que mais concorreu para a dissolução da diferença, e, assim, ao bloqueio à constituição de uma teoria da representação que combinasse dialética e ontologia do espaço, tal como parece agora emergir com a liberação ontológico-ôntica da diferença. Palavras-chave: diferença, identidade, dialética.Abstract Resting its axis on the identity discourse has made geography one of the knowledge fields which most contributed to the dissolution of difference and, hence, to obstruct a representation theory constitution, which would combine dialectics and space ontology, as it looks to emerge now with the difference ontological-ontic liberation. Keywords: difference, identity, dialetics.

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