Related papers: Classification of linearly compact simple N=6 3-al…
In our previous paper we classified linearly compact algebraic simple N=6 3-algebras. In the present paper we classify their "physical" counterparts, which actually appear in the N=6 supersymmetric 3-dimensional Chern-Simons theories.
We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras…
We use superalgebras to realize the 3-algebras used to construct N=6, 8 Chern-Simons-matter (CSM) theories. We demonstrate that the superalgebra realization of the 3-algebras provides a unified framework for classifying the gauge groups of…
The three-algebras used by Bagger and Lambert in N=6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems…
In this work we present 3-algebraic constructions and representations for three-dimensional N = 5 supersymmetric Chern-Simons theories, and show how they relate to theories with additional supersymmetries. The N = 5 structure constants give…
We write the Lagrangian of the general N=5 three-dimensional superconformal Chern-Simons theory, based on a basic Lie superalgebra, in terms of our recently introduced N=5 three-algebras. These include N=6 and N=8 three-algebras as special…
The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalisation of the notion of a Lie (resp. Jordan) superalgebra. Intuitively rigidity means that small deformations of the product under the structural…
In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then…
We derive the general form for a three-dimensional scale-invariant field theory with N=6 supersymmetry, SU(4) R-symmetry and a U(1) global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not…
We define a 3-algebra with structure constants being symmetric in the first two indices. We also introduce an invariant anti-symmetric tensor into this 3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal…
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…
We introduce the notion of universal odd generalized Poisson superalgebra associated to an associative algebra A, by generalizing a construction made in [5]. By making use of this notion we give a complete classification of simple linearly…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on…
We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…
We discuss a generalization of N=6 three-algebras to N=5 three-algebras in connection to anti-Lie triple systems and basic Lie superalgebras of type II. We then show that the structure constants defined in anti-Lie triple systems agree with…
There are thirteen types of three-dimensional Leibniz algebras over the real field $\mathbb{R}$ based on the classification given by S. Ayupov, B. Omirov and I. Rakhimov in [Leibniz algebras: structure and classification. CRC Press, Boca…
Under usual locality assumptions, we classify all non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries over $\mathbb{C}$: we single out 15 series (containing 2 analogs of contact series and one family…
We present all real solvable algebraically rigid Lie algebras of dimension $n\leq 8$. The difference between the classification of complex and real rigid Lie algebras is analyzed.
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…