Related papers: Lie 3-Algebra and Multiple M2-branes
In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether the algebra admits an idempotent or a pseudo-idempotent. We study the multiplicative…
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…
We obtain forms of Born-Infeld and D-brane actions that are quadratic in derivatives of $X$ and linear in $F_{\mu \nu}$ by introducing an auxiliary `metric' which has both symmetric and anti-symmetric parts, generalising the simplification…
In this paper, we investigate nilpotent Lie algebras $ L $ of nilpotency class $3 $ and provide a complete classification of those satisfying $ \dim L^2 = 3 $ and $Z(L) = L^3 \cong A(2). $ Furthermore, we explicitly characterize the…
We derive superalgebras in many types of supersymmetric M-brane backgrounds. The backgrounds examined here include the cases of the M-wave and the M-Kaluza-Klein monopole. On the basis of the obtained algebras, we deduce all the…
We study from the point of view of rational equivalence the enveloping algebras of Lie algebras of dimension 3 whose derived Lie subalgebra is of dimension 2, over an algebraically closed base field in arbitrary characteristics.
We demonstrate how a simple linear-algebraic technique used earlier to compute low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations,…
We introduce the notion of the modular class of a Lie algebroid equipped with a Nambu structure. In particular, we recover the modular class of a Nambu-Poisson manifold $M$ with its Nambu tensor $\Lambda$ as the modular class of the tangent…
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators…
We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy…
In this paper, we give the explicit structure of $ \otimes^{3} H $ and $ \wedge^{3} H $ where $ H $ is a generalized Heisenberg Lie algebra of rank at most $ 2. $ Moreover, for a non-abelian nilpotent Lie algebra $ L, $ we obtain an upper…
We propose a Lorentz covariant matrix model as a nonperturbative formulation of the bosonic M2-brane in M-theory. Unlike previous approaches relying on the light-cone gauge or symmetry-based constructions, our model retains full…
So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie--Poisson…
Automorphism, isomorphism, and embedding problems are investigated for a family of Nambu-Poisson algebras (or $n$-Lie Poisson algebras) using Poisson valuations.
We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the mass-deformed theory on N M2-branes: that there should be a set of discrete…
Starting from maximally supersymmetric (2+1)d Yang-Mills theory and using a duality transformation due to de Wit, Nicolai and Samtleben, we obtain the ghost-free Lorentzian 3-algebra theory that has recently been proposed to describe…
A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes…
We propose the study and description of the structure of complex Lie algebras with nilradical a nilpotent Lie algebra of type 2 by using sl2(C)-representation theory. Our results will be applied to review the classification given in [1] (J.…
A perturbative quantization procedure for Lie bialgebras is introduced and used to classify all three dimensional complex quantum algebras compatible with a given coproduct. The role of elements of the quantum universal enveloping algebra…
We propose a non-linear extension of U(1) \times U(1) (abelian) ABJM model including T_{M2} (higher derivative) corrections. The action proposed here is expected to describe a single M2-brane proving C^4/Z_k target space. The model includes…