Geodesic
Topological Hochschild $(\sigma,\tau)$-Cohomology Groups and $(\sigma,\tau)$-Super Weak Amenability of Banach Algebras
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 1, p. 145 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this work, we introduce the new cohomology groups depended on homomorphisms which are extensions of the topological Hochschild cohomology groups and investigate some of their properties that are analogue to the Hochschild cohomology groups. In addition, we use some homomorphisms on Banach algebras to define a new concept of amenability, namely, $(\sigma,\tau)$-super weak amenability which is a generalization of the cyclic amenability. Finally, we show that this new notion on a commutative Banach algebra ${\mathcal A}$ is equivalent to the $(\sigma,\tau)$-weak amenability, where $\sigma$ and $\tau$ are some continuous homomorphisms on ${\mathcal A}$.
Classification : 46H25 47B47
Keywords: $(\sigma;\tau)$-derivation, $(\sigma;\tau)$-inner derivation, $(\sigma;\tau)$-amenability, $(\sigma;\tau)$-contractibility, approximate identity, Banach algebra, Banach module 
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     title = {Topological {Hochschild} $(\sigma,\tau)${-Cohomology} {Groups} and $(\sigma,\tau)${-Super} {Weak} {Amenability} of {Banach} {Algebras}},
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Abolfazl Niazi Motlagh; Maryam Khosravi; Abasalt Bodaghi. Topological Hochschild $(\sigma,\tau)$-Cohomology Groups and $(\sigma,\tau)$-Super Weak Amenability of Banach Algebras. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 1, p. 145 . http://geodesic.mathdoc.fr/item/KJM_2020_44_1_a9/