Related papers: Generalized Yang Poisson Models on Canonical Phase…

Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequality in fractal space are investigated in detail.

For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the…

The applications of the general and reduced Yangian Y(sl(2)) and Y(su(3)) algebras are discussed. By taking a special constraint, the representation of Y(sl(2)) and Y(su(3)) can be divided into two 2 \times 2 and three 3 \times 3 blocks…

We prove several basic properties of the Yangian of the general linear Lie superalgebra.

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…

We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. We take a QP-manifold, i.e. a differential graded (dg) symplectic manifold, as a fundamental framework. A Poisson bracket in…

A class of Poisson algebras considered as a Poisson version of the multiparameter quantized coordinate rings of symplectic and Euclidean $2n$-spaces is constructed and the prime Poisson ideals and the symplectic ideals of these Poisson…

The phase structure of the generalized Yang--Mills theories is studied, and it is shown that {\it almost} always, it is of the third order. As a specific example, it is shown that all of the models with the interaction $\sum_j…

We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As consequences, we observe certain ring-theoretic invariants of the universal…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…

Most of pointed Hopf algebras of dimension $p^m$ with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations, homological dimensions and radicals of…

We introduce a new family of Poisson vertex algebras $\mathcal{W}(\mathfrak{a})$ analogous to the classical $\mathcal{W}$-algebras. The algebra $\mathcal{W}(\mathfrak{a})$ is associated with the centralizer $\mathfrak{a}$ of an arbitrary…

We prove that a Poisson-Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane. These formulas simultaneously generalize the classical Poisson formula and Newton…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained…

We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are…

We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…

We construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$. We also give the relationship between this homomorphism and…

The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of…