scholarly journals Generating degrees for graded projective resolutions

2018 ◽  
Vol 17 (10) ◽  
pp. 1850191 ◽  
Author(s):  
Eduardo N. Marcos ◽  
Andrea Solotar ◽  
Yury Volkov
Keyword(s):  
Tensor Products ◽  
Projective Resolution ◽  
Graded Algebras ◽  
Graded Modules ◽  
Projective Resolutions

We provide a framework connecting several well-known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras. Finally, we provide a tool to evaluate the possible degrees of a module appearing in a graded projective resolution once the generating degrees for the first term of some particular projective resolution are known.

scholarly journals Regular projective resolutions OF SEMIMODULES

2017 ◽  
Vol 126 (1B) ◽  
Author(s):  
Nguyễn Xuân Tuyến
Keyword(s):  
Comparison Theorem ◽  
Projective Resolution ◽  
Projective Resolutions

In this paper, we present an approach version of semimodule homologies by regular projective resolutions such as define a concept of a regular projective resolution, prove the comparison theorem for semimodules by these resolutions and based them provide cohomology monoids of semimodules.

Projective resolutions of graded modules

2001 ◽  
pp. 273-282
Author(s):  
Yves Félix ◽  
Stephen Halperin ◽  
Jean-Claude Thomas
Keyword(s):  
Graded Modules ◽  
Projective Resolutions

scholarly journals Sectional algebras of semigroupoid bundles

2020 ◽  
Vol 30 (06) ◽  
pp. 1257-1304
Author(s):  
Luiz Gustavo Cordeiro
Keyword(s):  
Direct Product ◽  
Tensor Products ◽  
Crossed Product ◽  
Direct Products ◽  
Crossed Products ◽  
Graded Algebras ◽  
Semidirect Products ◽  
Skew Products ◽  
Definition Of ◽  
Product Bundles

In this paper, we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell ([Formula: see text]-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be regarded as the sectional algebras of trivial (direct product) bundles. Several theorems which relate geometric and algebraic constructions — via the construction of a sectional algebra — are widely generalized: Direct products bundles by semigroupoids correspond to tensor products of algebras; semidirect products of bundles correspond to “naïve” crossed products of algebras; skew products of graded bundles correspond to smash products of graded algebras; Quotient bundles correspond to quotient algebras. Moreover, most of the results hold in the non-Hausdorff setting. In the course of this work, we generalize the definition of smash products to groupoid graded algebras. As an application, we prove that whenever [Formula: see text] is a ∧-preaction of a discrete inverse semigroupoid [Formula: see text] on an ample (possibly non-Hausdorff) groupoid [Formula: see text], the Steinberg algebra of the associated groupoid of germs is naturally isomorphic to a crossed product of the Steinberg algebra of [Formula: see text] by [Formula: see text]. This is a far-reaching generalization of analogous results which had been proven in particular cases.

Tensor Products of Graded Algebras and Unique Factorization

1979 ◽  
Vol 101 (4) ◽  
pp. 909 ◽  
Author(s):  
Richard Body ◽  
Roy Douglas
Keyword(s):  
Tensor Products ◽  
Unique Factorization ◽  
Graded Algebras

COHOMOLOGY AND HOMOLOGY OF ABELIAN GROUPS GRADED KOSZUL–VINBERG ALGEBRAS

2009 ◽  
Vol 06 (02) ◽  
pp. 241-266 ◽  
Author(s):  
MICHEL NGUIFFO BOYOM ◽  
F. NGAKEU
Keyword(s):  
Abelian Groups ◽  
Graded Algebras ◽  
Graded Modules ◽  
Vinberg Algebras

We study abelian groups graded (or color) Koszul–Vinberg algebras and their modules. Koszul–Vinberg cohomology and homology of these algebras are studied. As applications, we investigate some extensions of graded algebras and graded modules.

scholarly journals Regular projective resolutions OF SEMIMODULES

2017 ◽  
Vol 126 (1B) ◽  
pp. 43
Author(s):  
Ho Xuan Thang ◽  
Nguyen Xuan Tuyen
Keyword(s):  
Comparison Theorem ◽  
Projective Resolution ◽  
Projective Resolutions

In this paper, we present an approach version of semimodule homologies by regular projective resolutions such as define a concept of a regular projective resolution, prove the comparison theorem for semimodules by these resolutions and based them provide cohomology monoids of semimodules.

scholarly journals NON-COMMUTATIVE CONNECTIONS OF THE SECOND KIND

2008 ◽  
Vol 07 (05) ◽  
pp. 557-573 ◽  
Author(s):  
TOMASZ BRZEZIŃSKI
Keyword(s):  
Chain Complex ◽  
Tensor Products ◽  
Graded Algebras ◽  
Principal Bundles ◽  
Induction Procedure ◽  
Differential Graded Algebras ◽  
A Chain

A connection-like objects, termed hom-connections are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a differentiable bimodule is described. The curvature for a hom-connection is defined, and it is shown that flat hom-connections give rise to a chain complex.

scholarly journals Homotopism of Homological Complexes over Nonassociative Algebras with Metagroup Relations

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 734
Author(s):  
Sergey Victor Ludkowski
Keyword(s):  
Tensor Products ◽  
Graded Modules ◽  
Nonassociative Algebras

The article is devoted to homological complexes. Smashly graded modules and complexes are studied over nonassociative algebras with metagroup relations. Smashed tensor products of homological complexes are investigated. Their homotopisms and homologisms are scrutinized.

DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS

2003 ◽  
Vol 68 (02) ◽  
pp. 288-306 ◽  
Author(s):  
ANDERS FRANKILD ◽  
SRIKANTH IYENGAR ◽  
PETER JØRGENSEN
Keyword(s):  
Graded Algebras ◽  
Graded Modules ◽  
Differential Graded Algebras

scholarly journals Projective resolutions for graph products

1995 ◽  
Vol 38 (1) ◽  
pp. 185-188 ◽  
Author(s):  
Daniel E. Cohen
Keyword(s):  
Normal Subgroup ◽  
Free Product ◽  
Finite Graph ◽  
Projective Resolution ◽  
Graph Products ◽  
Graph Product ◽  
Projective Resolutions

Let Γ be a finite graph together with a group Gv at each vertex v. The graph productG(Γ) is obtained from the free product of all Gv by factoring out by the normal subgroup generated by for all adjacent v, w.In this note we construct a projective resolution for G(Γ) given projective resolutions for each Gv, and obtain some applications.

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