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

The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…

In this paper, we generalize the Tits construction for Lie superalgebras such that $\mathfrak{sl}_2$ acts by even derivations and decompose, as $\mathfrak{sl}_2$-module, into a direct sum of copies of the adjoint, the natural and the…

Let $E\supseteq F$ be a field extension and $M$ a graded Lie algebra of maximal class over $E$. We investigate the $F$-subalgebras $L$ of $M$, generated by elements of degree $1$. We provide conditions for $L$ being either ideally…

We classify all essential extensions of the form $$0 \rightarrow \W \rightarrow \D \rightarrow A \rightarrow 0$$ where $\W$ is the unique separable simple C*-algebra with a unique tracial state, with finite nuclear dimension and with…

Let $e$ be an arbitrary even nilpotent element in the general linear Lie superalgebra $\mathfrak{gl}_{M|N}$ and let $\mathcal{W}_e$ be the associated finite $W$-superalgebra. Let $Y_{m|n}$ be the super Yangian associated to the Lie…

We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness…

We consider a class of generalized Inonu-Wigner contraction for semidirect product of two particularly related semisimple Lie (super)algebras. The special class of such contractions provides D=4 Maxwell algebra and recently introduced…

A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner…

We develop a new method leading the structure of finite subsets S and T of an abelian group with $|S+T|\le |S|+|T|$. We show also how to recover the known results in this area in a relatively short space.

We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian reduction. In other words: we examine possible non-standard reality conditions for non-abelian…

In this paper we consider all consistent extensions of the AdS_5 x S^5 superalgebra, psu(2,2|4), to incorporate brane charges by introducing both bosonic and fermionic (non)central extensions. We study the Inonu-Wigner contraction of the…

A special symplectic Lie group is a triple $(G,\omega,\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure…

We obtain a new free field realization of $N=2$ super $W_{3}$ algebra using the technique of quantum hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra…

Let $\mathfrak{g}$ be a semisimple complex Lie algebra of finite dimension and $\mathfrak{h}$ be a semisimple subalgebra. We present an approach to find the branching rules for the pair $\mathfrak{g}\supset\mathfrak{h}$. According to an…

Motivated by recent progress on the correspondence between string theory on anti-de Sitter space and conformal field theory, we address the question of constructing space-time N extended superconformal algebras on the boundary of AdS_3.…

For any involution $\sigma$ of a semisimple Lie algebra $\mathfrak g$, one constructs a non-reductive Lie algebra $\mathfrak k$, which is called a $\mathbb Z_2$-contraction of $\mathfrak g$. In this paper, we attack the problem of…

Methods are reviewed for computing the instanton expansion of the prepotential for N=2 Seiberg-Witten (SW) theory with non-hyperelliptic curves. These results, if compared with the instanton expansion obtained from the microscopic…

In this paper, we study the construction of the supersymmetric extensions of vertex algebras. In particular, for $N = n \in \mathbb{Z}_{+}$, we show the universal enveloping $N = n$ supersymmetric (SUSY) vertex algebra of an $N = n$ SUSY…

Applying an efficient pattern-based computational method of generating the so-called 'resonating' algebraic structures results in a broad class of the new Lie (super)algebras. Those structures inherit the AdS base (anti)commutation pattern…

An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \land p = q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AE-subclasses of…