Related papers: Miniversal deformations of dialgebras
We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.
Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…
We construct a versal family of deformations of CR structures in five dimensions, using a differential complex closely related to the differential form complex introduced by Rumin for contact manifolds.
We introduce a new type of deformation of the chiral symmetry based on the deformation of the Laurent expansion of the conformal energy momentum tensor. Two kinds of solutions of the deformed equations of continuity are worked out. Known…
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
In this work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz…
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
We obtain a complete classification of minimal simple unitary $W$-algebras.
We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. We emphasize the use of several types of dynamical variables : branches, power sums and…
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove…
In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…
We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.
All complex $3$-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex $3$-dimensional nilalgebras were obtained.
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
A construction of the tangent dg Lie algebra of a sheaf of operad algebras on a site is presented. The requirements on the site are very mild; the requirements on the algebra are more substantial. A few applications including the…
We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…