相关论文: Infinite S-Expansion with Ideal Subtraction and So…

We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…

In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation $\D$ of any Lie algebra $\g$. Here it is shown how infinite dimensional Lie algebras appear naturally…

Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

Given a subset $S=\{s_0, s_1\}$ of the complex plane with two points and an infinite subset ${\mathscr S}$ of $S\times {\mathbb N}$, where ${\mathbb N}=\{0,1,2,\dots\}$ is the set of nonnegative integers, we ask for a lower bound for the…

This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…

Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of…

We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form…

Given a unital associative ring S and a subring R, we say that S is an ideal (or Dorroh) extension of R if for some ideal I of S, S = R + I, where the sum is direct. In this note we investigate the ideal structure of an arbitrary ideal…

Given a countable group $X$ we study the algebraic structure of its superextension $\lambda(X)$. This is a right-topological semigroup consisting of all maximal linked systems on $X$ endowed with the operation $$\mathcal A\circ\mathcal…

Inspired by results for graph $C^*$-algebras, we investigate connections between the ideal structure of an inverse semigroup $S$ and that of its tight $C^*$-algebra by relating ideals in $S$ to certain open invariant sets in the associated…

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…

The central extension of a new infinite dimensional algebra which has both $W_\infty$ and affine $sl(2,R)$ as subalgebras is found. The critical dimension of the corresponding string model is $D=5$.

A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it coincides with its idealizer IL(S). In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.

The super-AdS_5 X S^5 and the four-dimensional N=4 superconformal algebras play important roles in superstring theories. It is often discussed the roles of the osp(1|32) algebra as a maximal extension of the superalgebras in flat…

In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…

In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $\mathfrak{so}\left(2,2\right)$ algebra. We show that the Lie algebra expansion method based on semigroups reproduces not…

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were…

In this paper we extend the characterisation of kernels in semirings as subtractive ideals to general algebras. We then analyse the counterparts of ``subtractive'' and ``ideal'' in several different algebraic settings.