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Left-right noncommutative Poisson algebras

José Casas, Tamar Datuashvili, Manuel Ladra (2014)

Open Mathematics

The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as...

Les ( a , b ) -algèbres à homotopie près

Walid Aloulou (2010)

Annales mathématiques Blaise Pascal

On étudie dans cet article les notions d’algèbre à homotopie près pour une structure définie par deux opérations . et [ , ] . Ayant déterminé la structure des G ∞ algèbres et des P ∞ algèbres, on généralise cette construction et on définit la stucture des ( a , b ) -algèbres à homotopie près. Etant donnée une structure d’algèbre commutative et de Lie différentielle graduée pour deux décalages des degrés donnés par a et b , on donnera une construction explicite de l’algèbre à homotopie près associée et on précisera...

Localization and colocalization in tilting torsion theory for coalgebras

Yuan Li, Hailou Yao (2021)

Czechoslovak Mathematical Journal

Tilting theory plays an important role in the representation theory of coalgebras. This paper seeks how to apply the theory of localization and colocalization to tilting torsion theory in the category of comodules. In order to better understand the process, we give the (co)localization for morphisms, (pre)covers and special precovers. For that reason, we investigate the (co)localization in tilting torsion theory for coalgebras.

Loop cohomology

Kenneth Walter Johnson, Charles R. Leedham-Green (1990)

Czechoslovak Mathematical Journal

Minimal finite models.

Barmak, Jonathan Ariel, Minian, Elias Gabriel (2007)

Journal of Homotopy and Related Structures

Minimal resolutions and other minimal models.

Agustí Roig (1993)

Publicacions Matemàtiques

In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes....

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