This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

The Landau problem in the noncommutative plane is discussed in the context of realizations of the two-fold centrally extended planar Galilei group and the anyon theory. In 2+1 dimensions, Galilei group admits a two-fold central extension [1, 2] characterized by the algebra with the nonzero Poisson bracket relations {Ki,Pj} = mδij, {Ki,Kj} = −κǫij , (1) {Ki,H} = Pi, {J ,Pi} = ǫijPj , {J ,Ki} = ǫ...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

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, in particular isomorphic to the angular momentum algebra. The work is in the spirit of our earlier works in this connection, i.e. PLB 618 (2005)243 and PLB 623 (2005)251, where the κ-Minkowski form of noncomutative spacetime was consider...

The standard C*–algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C*–algebra of the canonical commutation relations ...

We construct two possible candidates for the non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. The bms4 algebra is infinitedimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinitedimensional extensions...

We demonstrate that the one-loop exact subleading soft graviton theorem automatically follows from conservation of BMS charges, provided hard and fluxes separately represent extended algebra at null infinity. This confirms superrotations are genuine symmetries gravitational $\mathcal{S}$-matrix beyond semiclassical regime. In contrast with a previous proposal, celestial stress-tensor accounting...