Related papers: A generalized super integrable hierarchy of Dirac …
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…
We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple Z-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain…
A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre series expansion of the transmutation kernel. A linear…
A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related…
The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…
Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension…
For a root system of type $B$ we study an algebra similar to a graded Hecke algebra, isomorphic to a subalgebra of the rational Cherednik algebra. We introduce principal series modules over it and prove an irreducibility criterion for these…
We give a representation--theoretic interpretation of recent discovered coupled soliton equations using vertex operators construction of affinization of not simple but quadratic Lie algebras. In this setup we are able to obtain new…
In this paper, we shall classify ``quadratic'' conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra.Four general constructions of such pairs are given. Moreover, we shall classify such pairs…
Let $\mathbb{k}$ be an algebraically closed field of characteristic $ p>0. $ In this short note, we illustrate a class of Lie superalgebras over $ \mathbb{k} $ such that the category of restricted supermodules is of one block. As an…
In this paper, we introduce two new families of infinite-dimensional simple Lie algebras and a new family of infinite-dimensional simple Lie superalgebras. These algebras can be viewed as generalizations of the Block algebras.
The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal reducible graded subalgebras are described completely and their isomorphism classes,…
A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved…
Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and…
We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the…
In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either…
In this paper, at first the construction of Lie higher derivations and higher derivations on a generalized matrix algebra were characterized; then the conditions under which a Lie higher derivation on generalized matrix algebras is proper…
The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial…