Related papers: Multi-operator brackets acting thrice
Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu…
The Grassmann-odd Nambu-like brackets corresponding to an arbitrary Lie superalgebra and realized on the supermanifolds are proposed.
In this article we give a concise review of recent progress in our understanding of the Lie 3-algebra and their application to the Bagger-Lambert-Gustavsson model describing multiple M2-branes in M theory.
The Grassmann-odd Nambu-like bracket corresponding to an arbitrary Lie algebra and realized on the Grassmann algebra is proposed.
The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed.
Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new…
A simplified version of 3d BL theory is considered, which allows any number N of M2 branes in d=11. The underlying 3-algebra structure is provided by degenerate U(N) Nambu bracket [X,Y,Z] = tr(X) [Y,Z] + tr(Y) [Z,X] + tr(Z) [X,Y], the…
It is shown that the manifold S^3 can be equipped with a natural Nambu structure arising out of a cross product on the tangent space. Further, the group action of SU(2) on S^3 is shown to be Nambu action. Moreover, we compare the action of…
Mizuno provided 19 examples of generalized rank three Nahm sums with symmetrizer $\mathrm{diag}(1,1,2)$ which are conjecturally modular. We confirm their modularity by establishing Rogers--Ramanujan type identities of index $(1,1,2)$ for…
We introduce an n-ary Lie algebroid canonically associated with a Nambu-Poisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize…
The dynamics of topological open branes is controlled by Nambu Brackets. Thus, they might be quantized through the consistent quantization of the underlying Nambu brackets, including odd ones: these are reachable systematically from even…
While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in…
We construct ternary self-distributive (TSD) objects from compositions of binary Lie algebras, $3$-Lie algebras and, in particular, ternary Nambu-Lie algebras. We show that the structures obtained satisfy an invertibility property…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this large family there is a subfamily of interpolation-like identities discovered by Hermite and revived rather recently…
An alternative and combinatorial proof is given for a connection between a system of Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
We show that there exists a cut-off version of Nambu-Poisson bracket which defines a finite dimensional Lie 3-algebra. The algebra still satisfies the fundamental identity and thus produces N=8 supersymmetric BLG type equation of motion for…
We make an exhaustive study of the properties of multiplication operator $M_u$ acting on K\"othe spaces. We characterize the multiplication operators, acting on K\"othe spaces, which are: bounded, injective, onto, bijective, Fredholm,…
We study a commuting triple of bounded operators $(A, B, P)$ which has the tetrablock as a spectral set.