Our interest in this work is group extensions of minimal flows with compact abelian groups the fibres. We study their structure from categorical and algebraic points view, describe relations dynamics to one-dimensional algebraic-

Abelian deformations of ordinary algebras of functions are studied. The role of Harrison cohomology in classifying such deformations is illustrated in the context of simple examples chosen for their relevance to physics. It is well known that Harrison cohomology is trivial on smooth manifolds and that, consequently, abelian ∗-products on such manifolds are trivial to first order in the deformat...

Abelian deformations of ordinary algebras of functions are studied. The role of Harrison cohomology in classifying such deformations is illustrated in the context of simple examples chosen for their relevance to physics. It is well known that Harrison cohomology is trivial on smooth manifolds and that, consequently, abelian ∗-products on such manifolds are trivial to first order in the deformat...

Abelian deformations of ordinary algebras of functions are studied. The role of Harrison cohomology in classifying such deformations is illustrated in the context of simple examples chosen for their relevance to physics. It is well known that Harrison cohomology is trivial on smooth manifolds and that, consequently, abelian ∗-products on such manifolds are trivial to first order in the deformat...

The first-order correction to the one-form sector of equations $3d$ higher-spin theory is derived from generating nonlinear HS system by virtue shifted homotopy approach. family solutions that disentangles for dynamical and topological fields in first order perturbation found. This shown belong different cohomology class compared solution found earlier direct methods. related be same as underly...

We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only the generalized cohomology theory represented by tensor unit object classes. also stable $\mathbb{A}^1$-derived does not admit oriented and, more generally, symplectic bundles. In order to do so we compute first homology sheaves of sphere spectrum class i...