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Register a new userThe deformations of antibracket with even and odd deformation parameters, defined on the space DE_1
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We consider antiPoisson superalgebra realized on the smooth Grassmann-valued functions of the form xi f_0(x)+f_1(x), where f_0 has compact support on R, and with the parity opposite to that of the Grassmann superalgebra realized on these functions. The deformations with even and odd deformation parameters of this superalgebra are found.
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We consider antibracket superalgebras realized on the smooth Grassmann-valued functions with compact supports in n-dimensional space and with the grading inverse to Grassmanian parity. The deformations with even and odd deformation parameters of these superalgebras are presented for arbitrary n.
We consider antiPoisson superalgebras realized on the smooth Grassmann-valued functions with compact supports in R^n and with the grading inverse to Grassmanian parity. The deformations of these superalgebras and their central extensions are found.
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the multidifferential ones, and consider their infinite order jet prolongation. The infinite order jet manifold is endowed with the canonical flat connection that provides the covariant formula of a deformation star-product.
In this paper, we show that it is always possible to deform a differential equation $partial_x Psi(x) = L(x) Psi(x)$ with $L(x) in mathfrak{sl}_2(mathbb{C})(x)$ by introducing a small formal parameter $hbar$ in such a way that it satisfies the Topological Type properties of Berg`ere, Borot and Eynard. This is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce $hbar$. The topological recursion is then proved to provide a formal series expansion of the corresponding tau-function whose coefficients can thus be expressed in terms of intersections of tautological classes in the Deligne-Mumford compactification of the moduli space of surfaces. We present a few examples including any Fuchsian system of $mathfrak{sl}_2(mathbb{C})(x)$ as well as some elements of Painleve hierarchies.
Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfelds twisting tensor technique. The other one relies on an appropriate extension of deformed realizations of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers kappa-Poincare dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincare algebra) takes an energy-dependent linear mass deformation form.
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