相关论文: Deformation Theory of Infinity Algebras
This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…
The importance of the first-class constraint algebra of general relativity is not limited just by its self-contained description of the gauge nature of spacetime, but it also provides conditions to properly evolve the geometry by selecting…
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying…
In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation…
Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced by Tao Zhang and Juan Li . We extend their theory to develop formal one-parameter deformation theory of Lie-Yamaguti algebras. It turns out that the right deformation…
Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that…
In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal…
In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in…
In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
Let $f$ be a Hochschild $2$-cocycle and let $A_f$ be an infinitesimal deformation of an associative finite dimensional algebra $A$ over an algebraically closed field $\Bbbk$. We investigate the algebra structure of the Ext-algebra of $A_f$…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
Any deformation of a Weyl or Clifford algebra can be realized through some change of generators in the undeformed algebra. Here we briefly describe and motivate our systematic procedure for constructing all such changes of generators for…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
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…
We start studying chiral algebras (as defined by A. Beilinson and V. Drinfeld) from the point of view of deformation theory. First, we define the notion of deformation of a chiral algebra on a smooth curve $X$ over a bundle of local…