Related papers: Miniversal deformations of dialgebras
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
In this paper, deformations of $L_\infty$-algebras are defined in such a way that the bases of deformations are $L_\infty$-algebras, as well. A universal and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose…
In this paper, for a given variety $\Var$, we present a universal algorithm for constructing a subvariety of $\Var$-dialgebras from which one can recover an algebra belonging to $\Var$. Such a subvariety is called the variety of initial…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup -- these curves make up a notable family of complete intersection monomial curves. First, we dispense a…
This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
A practical method for constructing a nontrivial homomorphsim between Verma modules is described.
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…
We realize the free dendriform trialgebra on one generator, as well as several other examples of dendriform trialgebras, as sub-trialgebras of an algebra of noncommutative polynomials in infinitely many variables.
We prove thst the deformation complex of a d-algebra (shifted by 1-d) carries a natural structure of (d+1)-algebra. This is a purely algebraic version of a similkar theorem of Kontsevich.
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give…
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…