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On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, V. Miemietz (2010)

Colloquium Mathematicae

We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when this category...

On category 𝒪 for cyclotomic rational Cherednik algebras

Iain G. Gordon, Ivan Losev (2014)

Journal of the European Mathematical Society

We study equivalences for category 𝒪 p of the rational Cherednik algebras 𝐇 p of type G ℓ ( n ) = ( μ ℓ ) n ⋊ 𝔖 n : a highest weight equivalence between 𝒪 p and 𝒪 σ ( p ) for σ ∈ 𝔖 ℓ and an action of 𝔖 ℓ on an explicit non-empty Zariski open set of parameters p ; a derived equivalence between 𝒪 p and 𝒪 p ' whenever p and p ' have integral difference; a highest weight equivalence between 𝒪 p and a parabolic category 𝒪 for the general linear group, under a non-rationality assumption on the parameter p . As a consequence, we confirm special cases of conjectures...

On centralizers of semiprime rings

Borut Zalar (1991)

Commentationes Mathematicae Universitatis Carolinae

Let 𝒦 be a semiprime ring and T : 𝒦 → 𝒦 an additive mapping such that T ( x 2 ) = T ( x ) x holds for all x ∈ 𝒦 . Then T is a left centralizer of 𝒦 . It is also proved that Jordan centralizers and centralizers of 𝒦 coincide.

On certain classes of modules.

Kalathoor Varadarajan (1992)

Publicacions Matemàtiques

Let X be a class or R-modules containing 0 and closed under isomorphic images. With any such X we associate three classes ΓX, FX and ΔX. The study of some of the closure properties of these classes allows us to obtain characterization of Artinian modules dualizing results of Chatters. The theory of Dual Glodie dimension as developed by the author in some of his earlier work plays a crucial role in the present paper.

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