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$n$ -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

Let $R$ be a graded ring and $n \geq 1$ an integer. We introduce and study $n$ -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that $n$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be $m$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever $n > m$ . Many properties of the $n$ -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...

Non-abelian cohomology of associative algebras. The $9$ -term exact sequence

Antonio M. Cegarra, Antonio R. Garzon (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Non-abelian cohomology of groups.

Inassaridze, H. (1997)

Georgian Mathematical Journal

Non-abelian cohomology via parity quasi-complexes.

Ionescu, Lucian M. (2004)

Homology, Homotopy and Applications

Non-abelian cohomology with coefficients in crossed bimodules.

Inassaridze, H. (1997)

Georgian Mathematical Journal

Non-abelian tensor and exterior products modulo $q$ and universal $q$ -central relative extension of Lie algebra.

Khmaladze, Emzar (1999)

Homology, Homotopy and Applications

Non-abelian tensor product of Lie algebras and its derived functors.

Nick Inassaridze, Emzar Khmaladze, Manuel Ladra (2002)

Extracta Mathematicae

Non-commutative differential geometry

Alain Connes (1985)

Publications Mathématiques de l'IHÉS

Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ${(k)}_{F}$ of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ${(k)}_{F}$ is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...

Nondegenerate cohomology pairing for transitive Lie algebroids, characterization

Jan Kubarski, Alexandr Mishchenko (2004)

Open Mathematics

The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...