let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

We develop homological techniques for finding explicit combinatorial formulas for finite-type cohomology classes of spaces of knots in R, n ≥ 3, generalizing the Polyak—Viro formulas [9] for invariants (i.e., 0-dimensional cohomology classes) of knots in R. As the first applications, we give such formulas for the (reduced mod 2) generalized Teiblum—Turchin cocycle of order 3 (which is the simpl...

The goal of this paper is to study cohomological theory n-Lie algebras with derivations. We define the representation an n-LieDer pair and consider its cohomology. Likewise, we verify that a cohomology could be derived from associated LeibDer pair. Furthermore, discuss (n−1)-order deformations Nijenhuis operator pairs. central extensions pairs are also investigated in terms first groups coeffic...

We obtain generalizations of some results of Turaev from [Tur02]. Turaev’s results relate leading order terms of the Turaev torsion of closed, oriented, connected 3–manifolds to certain “determinants” derived from cohomology operations such as the alternate trilinear form on the first cohomology group given by cup product. These determinants unfortunately do not generalize directly to compact, ...

This question is rather old [3]: Which groups having periodic cohomology can act freely on some homotopy sphere? The first nontrivial restriction was supplied by Milnor in [3]. Every element of order two must lie in the center. Swan [ô] showed that any group with periodic cohomology acts freely on a c.w. complex of the homotopy type of sphere. If the group has odd order then it is metacyclic. T...

1. Interval positroid varieties 1 1.1. Schubert varieties 1 1.2. Schubert calculus 2 1.3. First positivity result 3 1.4. Interval rank varieties 5 2. Vakil’s Littlewood-Richardson rule 7 2.1. Combinatorial shifting 7 2.2. Geometric shifting 7 2.3. Vakil’s degeneration order 9 2.4. Partial puzzles 10 3. Equivariant and Kextensions 11 3.1. K-homology 11 3.2. K-cohomology 12 3.3. Equivariant K-the...

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized sim...

We propose a simple but powerful approach to the verification of parameterised systems. The approach is based on modelling the reachability between parameterized states as deducibility between suitable encodings of states by formulae of first-order predicate logic. To establish a safety property, that is non-reachability of unsafe states, the finite model finder is used to find a finite counter...