scholarly journals Split exact sequences of finite MTL-chains

2021 ◽  
pp. 295-304
Author(s):  
J. L. Castiglioni ◽  
W. J. Zuluaga Botero
Keyword(s):  
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 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.

scholarly journals On exact sequences in the homology of groups and algebras

1970 ◽  
Vol 14 (2) ◽  
pp. 205-215 ◽  
Author(s):  
Beno Eckmann ◽  
Urs Stammbach
Keyword(s):  
Exact Sequences

scholarly journals Principal subspaces of twisted modules for certain lattice vertex operator algebras

2019 ◽  
Vol 30 (10) ◽  
pp. 1950048 ◽  
Author(s):  
Michael Penn ◽  
Christopher Sadowski ◽  
Gautam Webb
Keyword(s):  
Algebraic Structure ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Gram Matrix ◽  
Vertex Operator Algebras ◽  
Generators And Relations ◽  
The Third ◽  
Exact Sequences

This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices [Formula: see text] whose Gram matrix contains only non-negative entries. We develop further ideas originally presented by Calinescu, Lepowsky, and Milas to find presentations (generators and relations) of the principal subspace of a certain natural twisted module for the vertex operator algebra [Formula: see text]. We then use these presentations to construct exact sequences involving this principal subspace, which give a set of recursions satisfied by the multigraded dimension of the principal subspace and allow us to find the multigraded dimension of the principal subspace.

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