Related papers: Deformations of M-theory Killing superalgebras
We describe the Lie algebra deformations of D=4 Maxwell superalgebra that was recently introduced as the symmetry algebra of a kappa-symmetric massless superparticle in a supersymmetric constant electromagnetic background. Further we…
The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study…
In this paper, enveloping Lie superalgebras of Bol superalgebras are introduced. The notion of Killing-Ricci forms and invariant forms of these superalgebras are investigated as generalization of the ones of Bol algebras.
We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…
We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special…
The near-horizon geometries of the spinning D3-, M2- and M5-branes are examined by the probes immersed in a co-rotating frame. It is found that the geometries become unstable at critical values of the spin angular velocity by emitting the…
The study of global deformations of Lie algebras is related to the problem of classification of simple Lie algebras over fields of small characteristic. The classification of finite-dimensional simple Lie algebras is complete over…
Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved $\mathbb{Z}/2$-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every $\mathbb{Z}/2$-graded simple Lie algebra in…
We show that the holonomy of the supercovariant connection for M-theory backgrounds with $N$ Killing spinors reduces to a subgroup of $SL(32-N,\bR)\st (\oplus^N \bR^{32-N})$. We use this to give the necessary and sufficient conditions for a…
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy analogues. Then…
We construct the Killing superalgebra of supersymmetric backgrounds of ten-dimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the…
We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with…
M5-branes wrapping a holomorphic curve in a Calabi-Yau manifold can be used to construct four-dimensional N=1 gauge theories. In this paper we will consider M5-brane configurations corresponding to N=2 theories broken to N=1 by a…
We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over \mathbb{C}. In particular, we describe all irreducible components of these varieties.
We discuss an SL(2,R) family of deformed N=2 four-dimensional gauge theories which we derive from a flux background in M-theory. In addition to the Omega-deformation this family includes a new deformation, which we call the…
We construct deformed, T^2 wrapped, rotating M2-branes on a resolved cone over Q^{1,1,1} and Q^{1,1,1}/Z_2, as well as on a product of two Eguchi-Hanson instantons. All worldvolume directions of these supersymmetric and regular solutions…
We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R^{1,9-n} x M_n with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS…
We find solutions of 11-dimensional supergravity for M5-branes wrapped on Riemann surfaces. These solutions preserve ${\cal N} = 2$ four-dimensional supersymmetry. They are dual to ${\cal N} = 2$ gauge theories, including non-conformal…
We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field…
We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…