Related papers: Biflatness of ${\ell}^1$-semilattice algebras

In this paper, we investigate the notion of approximate biprojectivity for semigroup algebras and for some Banach algebras related to semigroup algebras. We show that $\ell^{1}(S)$ is approximately biprojective if and only if $\ell^{1}(S)$…

We establish simplicial triviality of the convolution algebra $\ell^1(S)$, where $S$ is a band semigroup. This generalizes results of the first author [Glasgow Math. J. 2005, Houston J. Math. 2010]. To do so, we show that the cyclic…

The ${\ell}^1$-convolution algebra of a semilattice is known to have trivial cohom ology in degrees 1,2 and 3 whenever the coefficient bimodule is symmetric. We ex tend this result to all cohomology groups of degree $\geq 1$ with symmetric…

In this paper, we study the notion of $\phi$-biflatness for some Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that the Segal algebra $S(G)$ is left $\phi$-biflat if and only if $G$ is amenable. Also,…

Certain semigroups are known to admit a `strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the $\ell^1$-convolution algebras of such semigroups, and obtain a disintegration…

Let $S$ be a Rees semigroup, and let $\ell^1(S)$ be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of $\ell^1(S)$ is isomorphic to those of the underlying discrete group…

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group, G.

We investigate which weighted convolution algebras $\ell^1_\omega(S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson (JLMS, 1986). We give an explicit example where this is not the case. We show that the unweighted examples…

In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a…

We show that the biflatness - in the sense of A. Ya. Helemskii - of the Fourier algebra $A(G)$ of a locally compact group $G$ forces $G$ to either have an abelian subgroup of finite index or to be non-amenable without containing $F_2$, the…

In this paper we are going to investigate the approximate biprojectivity and the $\phi$-biflatness of some Banach algebras related to the locally compact groups. We show that a Segal algebra $S(G)$ is approximate biprojective if and only if…

We say that a formal deformation from an algebra $N$ to algebra $A$ is strongly flat if for every real number $e $ there is a real number $0<s<e$ such that this deformation specialised at $t=s$ gives an algebra isomorphic to $A$. We show…

Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…

In this paper, we countinue our work in \cite{11}. We show that $L^{1}(G,w)$ is $\phi_{0}$-biprojective if and only if $G$ is compact, where $\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability…

Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $\sigma$ on it, the notion of $\sigma$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The…

Amenability and pseudo-amenability of $ \ell^{1}(S,\omega) $ is characterized, where $S$ is a left (right) zero semigroup or it is a rectangular band semigroup. The equivalence conditions to amenability of $\ell^{1}(S,\omega)$ are provided,…

In this paper, we study the notion of approximately bi at Banach algebras for second dual Banach algebras and semigroup algebras. We show that for a locally compact group G, if S(G)?? is approximately bi at, then G is amenable group. Also…

This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…

Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps between them, called the convolution algebra of C and A. In…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…