Related papers: An integrable hierarchy associated with loop exten…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We study finite dimensional almost and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and…
We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module…
It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of…
The integrable (2+1)-dimensional chiral equations are related to the self-dual Yang-Mills equation. Previously-known nonlocal conservation laws do not yield finite conserved charges, because the relevant spatial integrals diverge. We…
The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability. The well-known modified KdV equation is a prototypical example of integrable…
To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods which are based on integrable scalar nonlinear partial…
In the present contribution, I report on certain {\it non-linear} and {\it non-local} extensions of the conformal (Virasoro) algebra. These so-called $V$-algebras are matrix generalizations of $W$-algebras. First, in the context of…
We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of $2d$ integrable models. These Lie algebras are defined by the set of infinitesimal, nonlinear, and…
A chiral $(N,0) $ supergravity theory in d=2 dimensions for any $N$ and its induced action can be obtained by constraining the currents of an Osp(N$|$2) WZWN model. The underlying symmetry algebras are the nonlinear SO(N) superconformal…
In this note, we calculate all untwisted and twisted (Z/2)^n-equivariant K-groups with compact supports of real finite-dimensional linear representations of (Z/2)^n. The question was motivated by the question of D-brane charges for orbifold…
We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3…
In this paper, by considering two non-isospectral problems with matrices chosen on the color Lie algebra $\mathfrak{sp}_{1}(6)$, we construct (1+1)-dimensional and (2+1)-dimensional super integrable systems on $\mathfrak{sp}_{1}(6)$.…
Employing the Hirota's method, a class of soliton solutions for the N=2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations connected…
Integrable $\sigma$-models, such as the principal chiral model, ${\mathbb{Z}}_T$-coset models for $T \in {\mathbb{Z}}_{\geq 2}$ and their various integrable deformations, are examples of non-ultralocal integrable field theories described by…
An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and…
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…
We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in arXiv:1705.04410. In contrast to the simply laced quivers, here two $\Omega$-background parameters play different roles, so that we can…
To every partition $n=n_1+n_2+\cdots+n_s$ one can associate a vertex operator realization of the Lie algebras $a_{\infty}$ and $\hat{gl}_n$. Using this construction we make reductions of the $s$--component KP hierarchy, reductions which are…
We define twisted versions of the classical and quantum double ramification hierarchy construction based on intersection theory of the strata of meromorphic differentials in the moduli space of stable curves and $k$-twisted double…