相关论文: Extended deformation functors

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical…

We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…

We first give a short intrinsic, diagrammatic proof of the First Fundamental Theorem of invariant theory (FFT) for the special orthogonal group $\text{SO}_m(\mathbb{C})$, given the FFT for $\text{O}_m(\mathbb{C})$. We then define, by means…

This paper is devoted to the classification problems concerning extended deformations of convex polyhedra and real hyperplane arrangements in the following senses: combinatorial equivalence of face posets, normal equivalence on normal fans…

In this paper, we devote to extending structures for dendriform algebras. First, we define extending datums and unified products of dendriform algebras, and theoretically solve the extending structure problem. As an application, we consider…

The recent generalizations of Boltzmann-Gibbs statistics mathematically relies on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed…

We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a…

Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and…

We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…

We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of $N$-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object…

We extend the formalism of tri-vector deformations to the full SL(5) exceptional field theory with no truncation assumed thus covering 11D backgrounds of any form. We derive explicit transformation rules for 11D supergravity component…

Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel [Ha] proved that generalized tilting…

Using the theory of extensions of L-infinity algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the Chevalley-Eilenberg and Harrison…

We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…

We make a first step towards categorification of the dendriform operad, using categories of modules over the Tamari lattices. This means that we describe some functors that correspond to part of the operad structure.

We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets…

In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay…

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…