scholarly journals Jacobi–Zariski long nearly exact sequences for associative algebras

2021 ◽  
Author(s):  
Claude Cibils ◽  
Marcelo Lanzilotta ◽  
Eduardo N. Marcos ◽  
Andrea Solotar
Keyword(s):  
Associative Algebras ◽  
Exact Sequences

scholarly journals Corrigendum: Jacobi–Zariski long nearly exact sequences for associative algebras

2021 ◽  
Author(s):  
Claude Cibils ◽  
Marcelo Lanzilotta ◽  
Eduardo N. Marcos ◽  
Andrea Solotar
Keyword(s):  
Associative Algebras ◽  
Exact Sequences

The category of exact sequences of Banach spaces

2010 ◽  
pp. 139-158 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Yolanda Moreno
Keyword(s):  
Banach Spaces ◽  
Exact Sequences

scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Compatible O-operators on bimodules over associative algebras

2019 ◽  
Vol 532 ◽  
pp. 80-118 ◽  
Author(s):  
Jiefeng Liu ◽  
Chengming Bai ◽  
Yunhe Sheng
Keyword(s):  
Associative Algebras
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