Related papers: Generalised Bargmann Superalgebras
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We…
The aim of this paper is to generalise the construction of $3$-Bihom-Lie superalgebras and we provide some properties can be lifted to its $T^{\ast}$-extensions such as nilpotency, solvability and decomposition. We study the…
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
In this paper, first we classify non-abelian extensions of Leibniz algebras by the second non-abelian cohomology. Then, we construct Leibniz 2-algebras using derivations of Leibniz algebras, and show that under a condition on the center, a…
SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the…
We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and…
We obtain a recurrent and monotone method for constructing and classifying nilpotent Lie algebras by means of successive central extensions. It consists in calculating the second cohomology of an extendable nilpotent Lie algebra with the…
We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…
We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of…
In this paper, we investigate non-abelian extensions of Lie algebras with derivations using several different approaches. We show that the theory of non-abelian extensions of a Lie algebra with a derivation can be characterized by means of…
In this paper, we introduce the notion of a derivation of a Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of…
Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…
In 1983, Feingold and Frenkel discovered a relation between Siegel modular forms of genus two and a rank-three hyperbolic Kac--Moody algebra extending the affine Lie algebra of type $A_1$. It inspires a problem to explore more general…
The form of realistic space-time supersymmetry is fixed, by Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such…
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…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…
Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally…
We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…