Integrability of the one-dimensional Hubbard model and factorised scattering problem encountered on worldsheet AdS strings can be expressed in terms a peculiar quantum algebra. In this article, we derive classical limit these algebraic integrable structures based established results for exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) which form supersymmetric isomet...

We construct certain modified highest weight modules which are called quasi in this paper. Using the modules, we introduce a new category of over an affine Lie superalgebra contains projective covers. also prove that both these covers and satisfy vanishing property BRST cohomology.

A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson was established. Some non-trivial with a certain algebra (Witt algebra, $\mathcal{W}(a,-1)$, thin solvable abelian nilpotent radical) were constructed. In particular, we constructed an example the associative parts isomorphic to Laurent polynomials Witt algebra. On other side, it proven that there are no part se...

The aim of this work is to prove a technical result, that had been stated by Boyallian, Kac and Liberati \cite{ck6}, on the degree singular vectors finite Verma modules over exceptional Lie superalgebra $E(1,6)$ isomorphic annihilation associated with conformal $CK_{6}$.

I construct systems of generalized Pfaff equations (of the form α = 0, α some differential forms), preserved by the exceptional Lie superalgebras ksle(5|10), vle(3|6) and mb(3|8). This yields an intrinsic geometric definition of these algebras. The analogous construction for the contact superalgebra k(1|m) (a.k.a. the centerless N = m superconformal algebra) is reviewed.

We show that the poset of non-trivial partitions of {1, 2, . . . , n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σn and Σn+1 on the homology and cohomology of this partially-ordered set. AMS Classification 05E25; 17B60, 55P91

A model is presented for the structure and evolution of the eukaryotic and vertebrate mitochondrial genetic codes, based on the representation theory of the Lie superalgebra A(5; 0) ' sl(6=1). A key role is played by pyrimidine and purine exchange symmetries in codon quartets.

This paper generalize [7]: We construct new links in-variants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module. Using this, we get a multivariable link invariant associated to any one parameter family of irreducible g-modules.

We perform the bosonic dualisation of the matter coupled N = 1, D = 9 supergravity. We derive the Lie superalgebra which parameterizes the coset map whose Cartan form realizes the second-order bosonic field equations. Following the non-linear coset construction we present the first-order formulation of the bosonic field equations as a twisted self-duality condition.

The Z/2Z–graded intertwining operators are introduced. We study these operators in the case of “degenerate” N = 1 minimal models, with the central charge c = 3 2 . The corresponding fusion ring is isomorphic to the Grothendieck ring for the Lie superalgebra osp(1|2). We also discus multiplicity–2 fusion rules and logarithmic intertwiners.