Cyclic homology of group rings
We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Let 𝒯 be the Itô Hopf algebra over an associative algebra 𝓛 into which the universal enveloping algebra 𝓤 of the commutator Lie algebra 𝓛 is embedded as the subalgebra of symmetric tensors. We show that there is a one-to-one correspondence between deformations Δ[h] of the coproduct in 𝒯 and pairs (d⃗[h],d⃖[h]) of right and left differential maps which are deformations of the differential maps for 𝒯 [Hudson and Pulmannová, J. Math. Phys. 45 (2004)]. Corresponding to the multiplicativity and...
We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.