相关论文: Bimodule complexes via strong homotopy actions

We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…

This paper proposed a novel fully-actuated hexacopter. It features a dual-frame passive tilting structure and achieves independent control of translational motion and attitude with minimal actuators. Compared to previous fully-actuated…

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the…

We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group acts on that wheeled prop faithfully and…

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…

We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some…

If P is a dg-operad acting on a dg-algebra A via algebra homomorphisms, then P acts on the Hochschild complex of A. In the more general case when P is a dg-prop, we show that P still acts on the Hochschild complex, but only up to coherent…

We consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We obtain a description of their tangent bundles, compute their mod p…

Let $\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $\Lambda=\operatorname{End}_{\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal…

Controlling complex light waves to achieve desired behaviours or characteristics on demand presents a significant challenge. This task becomes even more complicated when manipulating speckled light beams owing to their inherently fuzzy…

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction…

We provide a complete classification of all tilting modules and tilting classes over almost perfect domains, which generalizes the classifications of tilting modules and tilting classes over Dedekind and 1-Gorenstein domains. Assuming the…

In this paper we study the category of graded modules for the current algebra associated to $\mathfrak{sl}_2$. The category enjoys many nice properties, including a tilting theory which was established in previous work of the authors. We…

We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.

We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasi-isomorphism…

We will invest quite some computer power to find double octic threefolds that are connected to weight four modular forms.

There is a growing need for robots that can change their shape, size and mechanical properties to adapt to evolving tasks and environments. However, current shape-changing systems generally utilize bespoke, system-specific mechanisms that…