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Left Frobenius Pairs,Cotorsion Pairs and Weak Auslander-Buchweitz Contexts in Triangulated Categories
《Algebra Colloquium》2024年第2期285-308,共24页Xin Ma Tiwei Zhao Zhaoyong Huang Nanqing Ding 
supported by the NSF of China(12001168,11901341,11971225,12171207);Henan University of Engineering(DKJ2019010);the Key Research Project of Education Department of Henan Province(21A110006);Youth Innovation Team of Universities of Shandong Province(2022KJ314).
Let T be a triangulated category with a proper classξof triangles.We introduce the notions of left Frobenius pairs,left(n-)cotorsion pairs and left(weak)Auslander-Buchweitz contexts with respect toξin T.We show how ...
关键词：left Frobenius pairs left n-cotorsion pairs left(weak)Auslander-Buchweitz contexts homological dimensions 
Categorizations of Limits of Grothendieck Groups over a Frobenius P-Category
《Algebra Colloquium》2022年第4期541-594,共54页Lluis Puig 
In[Frobenius Categories Versus Brauer Blocks,Progress in Math.,274]and in[Ordinary Grothendieck groups of a Frobenius P-category,Algebra Colloq.18(2011)1-76],we consider suitable inverse limits of Grothendieck groups ...
关键词：Frobenius category Grothendieckgroup perfect locality 
Generalized Centrosymmetric Matrix Algebras Induced by Automorphisms
《Algebra Colloquium》2022年第4期607-618,共12页Huabo Xu 
supported by Beijing Nova Program(Z181100006218010);by Research Ability Improvement Program of BUCEA(Grant No.X22026).
Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n...
关键词：φ-centrosymmetric matrix cellular algebra Frobenius extension 
Open Frobenius Cluster-Tilted Algebras
《Algebra Colloquium》2022年第1期1-22,共22页Viviana Gubitosi 
In this paper,we compute the Frobenius dimension of any cluster-tilted algebra of finite type.Moreover,we give conditions on the bound quiver of a cluster-tilted algebra A such that八has non-trivial open Frobenius str...
关键词：cluster-tilted algebras gentle algebras open Frobenius algebras nearly Probe-nius algebras 1 
Classification of Spherical Fusion Categories of Frobenius–Schur Exponent 2
《Algebra Colloquium》2021年第1期39-50,共12页Zheyan Wan Yilong Wang 
We thank Professor Siu-Hung Ng for helpful conversations.Z.Y.Wan is supported by the Shuimu Tsinghua Scholar Program.
In this paper,we propose a new approach towards the classification of spherical fusion categories by their Frobenius–Schur exponents.We classify spherical fusion categories of Frobenius–Schur exponent 2 up to monoid...
关键词：spherical fusion category modular category Frobenius-Schur exponent Arf invariant Gauss sum 
A Correction to the Uniqueness of a Partial Perfect Locality over a Frobenius P-Category
《Algebra Colloquium》2019年第4期541-559,共19页Lluis Puig Jiping Zhang 
Let p be a prime,P a finite p-group and F a Frobenius P-category.In[Existcnee,uniqueness and functoriality of the perfect locality over a Frobenius P-category,Algebra Colloq.23(2016)541-622],we claimed the uniqueness ...
关键词：group P-category local structure 
Existence, Uniqueness and Functoriality of the Perfect Locality over a Frobenius P-Category被引量：1
《Algebra Colloquium》2016年第4期541-622,共82页Lluis Puig 
Let p be a prime, P a finite p-group and F- a Frobenius P-category. The question on the existence of a suitable category L^scextending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes b...
关键词：group Frobenius P-category LOCALITY 
The Hecke Algebra of a Frobenius P-Category
《Algebra Colloquium》2014年第1期1-52,共52页Lluis Puig 
We introduce a new avatar of a Frobenius P-category F under the form of a suitable subring HF of the double Burnside ring of P -- called the Hecke algebra of F- where we are able to formulate： （i） the generalizatio...
关键词：finite group Frobenius category Hecke algebra Burnside ring 
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