相关论文: The Extension Structure of 2D Massive Current Alge…
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current $j_\mu$ associated with the global symmetry of the theory, a composite…
Recently by Casas, Ladra and Rozikov a notion of a chain of evolution algebras is introduced. This chain is a dynamical system the state of which at each given time is an evolution algebra. The sequence of matrices of the structural…
In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra $R$ by a Leibniz conformal algebra $H$ and prove that all the non-abelian extensions are classified by non-abelian $2$nd cohomology $H^2_{nab}(R,H)$…
In this paper we consider the construction of a free differential algebra as an extension of the extended Bargmann algebra in arbitrary dimensions. This is achieved by introducing a new Maurer-Cartan equation for a three-form gauge…
Given a complex semisimple Lie algebra ${\mathfrak g}$ and a commutative ${\mathbb C}$-algebra $A$, let ${\mathfrak g}[A] = {\mathfrak g} \otimes A$ be the corresponding generalized current algebra. In this paper we explore questions…
We compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k<l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of…
We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification of diffeomorphism cocycles. We also…
The universal central extensions and their extension kernels of the matrix Lie superalgebra sl(m, n, A), the Steinberg Lie superalgebra st(m, n, A) in category {\bf SLeib} of Leibniz superalgebras are determined under a weak assumption…
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schr\"odinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the…
We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral…
We give two sufficient and necessary conditions for a Hochschild extension of a finite dimensional algebra by its dual bimodule and a Hochschild 2-cocycle to be a symmetric algebra.
We suggest an infinite-dimensional extension of the gauge transformations which includes non-Abelian tensor gauge fields. Extended gauge transformations of non-Abelian tensor gauge fields form a new large group which has natural geometrical…
We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an…
We propose an extension of the su(2,2|4) superalgebra to incorporate the $F1/D1$ string charges in type IIB string theory on the $AdS_{5} \times S^{5}$ background, or the electro-magnetic charges in the dual super Yang-Mills theory. With…
This paper presents a systematic study of the structure of non-solvable cyclic metric Lie algebras. A cyclic metric is a symmetric bilinear form satisfying a cyclic cocycle condition, which arises naturally in the contexts of…
We construct a general class of new time dependent solutions of non-linear sigma models coupled to gravity. These solutions describe configurations of expanding or contracting codimension two solitons which are not subject to a constraint…
This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras using and applies it to classify non-abelian extensions. The main result establishes that equivalence classes of split extensions of a Hom-Jacobi-Jordan algebra $J$ by…
In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six-dimensional superconformal field theories and we believe that they also underlie potential…
In this paper, we introduce the notions of crossed module of associative conformal algebras, 2-term strongly homotopy associative conformal algebras, and discuss the relationship between them and the 3-th Hochschild cohomology of…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…