The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature. The work is in the spirit of our earlier works in this connection, i.e. PLB 618 (2005)243 and PLB 623 (2005)251. This non-linear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantiz...

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...

A canonical quantization for two dimensional gravity models, including a dilaton gravity model, is performed in a way suitable for the light-cone gauge. We extend the theory developed by Abdalla et.al.[1] and obtain the correlation functions by using the screening charges of the symmetry algebra. It turns out that the role of the cosmological constant term in the Liouville theory is played by t...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

The notion of anyonic Wick algebras is introduced and the corresponding second quantisation procedure is discussed. Applications to the physics of 2D anyonic matter are presented. In particular the existence of thermodynamics in the in nite volume for the case of Leinaas-Myrheim potentials is presented. Additionally a new class of states corresponding to quasifree thermal states on some Wick al...

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin [11] quantization formalism is adopted in which the original sy...

We introduce a certain cellular algebra Q(n; r) which is a quotient of the q-Schur algebra S q (n; r). This is naturally equipped with a canonical basis which is compatible with Lusztig's canonical bases for certain modules for the quantized enveloping algebra U (sl n). We describe a diagram calculus for Q(n; r) which makes calculations involving the corresponding canonical bases easy to unders...

For an element x of the Cuntz algebra ON , define the isotropy subgroup Gx ≡ {g ∈ U(N) : αg(x) = x} of the unitary group U(N) with respect to the canonical action α of U(N) on ON . We have irreducible representations of the crossed product ONoGx by extending irreducible generalized permutative representations of ON and irreducible representation of Gx. ¿From this, the Peter-Weyl theorem for Gx ...