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We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation…

High Energy Physics - Theory · Physics 2012-02-28 Kumar S. Gupta , Stjepan Meljanac , Andjelo Samsarov

Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product. We also provide a desirable description of the subalgebra generated by the set of primitive elements of the quantum quasi-shuffle bialgebra. A…

Quantum Algebra · Mathematics 2011-12-06 Run-Qiang Jian

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we…

Mathematical Physics · Physics 2008-11-26 A. N. F. Aleixo , A. B. Balantekin , M. A. Candido Ribeiro

We describe the extension of the Wigner`s infinite-dimensional unitary representations of Poincar\'{e} group to the case of $\kappa$-deformed Poincar\'{e} group. We show that the corresponding coordinate wave functions on noncommutative…

High Energy Physics - Theory · Physics 2016-08-16 P. Kosiński , J. Lukierski , P. Maślanka

The aim of the paper is to answer the following question: does $\kappa$-deformation fit into the framework of noncommutative geometry in the sense of spectral triples? Using a compactification of time, we get a discrete version of…

Mathematical Physics · Physics 2011-09-20 B. Iochum , T. Masson , Th. Schücker , A. Sitarz

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

Operator Algebras · Mathematics 2007-05-23 Byung-Jay Kahng

In this paper, we investigate the Poincar\'e and discrete symmetries of a $\kappa$-deformed spin-$\tfrac12$ field, extending recent results obtained for scalar fields. We construct an action that is Poincar\'e invariant and analyze its…

High Energy Physics - Theory · Physics 2026-05-29 Tadeusz Adach , Andrea Bevilacqua , Jerzy Kowalski-Glikman , Giacomo Rosati , Wojciech Wiślicki

In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping…

Representation Theory · Mathematics 2024-02-07 Sanu Bera , Sugata Mandal , Soumendu Nandy

We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the…

Mathematical Physics · Physics 2017-07-11 Niklas Beisert , Reimar Hecht , Ben Hoare

We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed…

High Energy Physics - Theory · Physics 2011-07-19 Toshiaki Tanaka

A universal R--matrix for the quantum Heisenberg algebra h(1)q is presented. Despite of the non--quasitriangularity of this Hopf algebra, the quantum group induced from it coincides with the quasitriangular deformation already known.

High Energy Physics - Theory · Physics 2009-10-28 A. Ballesteros , Enrico Celeghini , F. J. Herranz , M. A. del Olmo , M. Santander

For finite semidistributive lattices the map $\kappa$ gives a bijection between the sets of completely join-irreducible elements and completely meet-irreducible elements. Here we study the $\kappa$-map in the context of torsion classes. It…

Representation Theory · Mathematics 2020-07-17 Emily Barnard , Gordana Todorov , Shijie Zhu

The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem context. The…

Mathematical Physics · Physics 2010-09-28 Roldao da Rocha , Alex E. Bernardini , Jayme Vaz

We study the commutators of the kappa-deformed Poincare Algebra (kappaPA) in an arbitrary basis. It is known that the two recently studied doubly special relativity theories correspond to different choices of kappaPA bases. We present…

High Energy Physics - Theory · Physics 2007-05-23 S. Kalyana Rama

The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…

High Energy Physics - Theory · Physics 2009-10-22 F. Bonechi , E. Celeghini , R. Giachetti , E. Sorace , M. Tarlini

We describe firstly the basic features of quantum $\kappa$-Poincar\'{e} symmetries with their Hopf algebra structure. The quantum $\kappa$-Poincar\'{e} framework in any basis relates rigidly the quantum $\kappa$-Poincar\'{e} algebra with…

High Energy Physics - Theory · Physics 2007-05-23 Jerzy Lukierski

We construct explicit examples of half-sided modular inclusions ${\mathcal N}\subset{\mathcal M}$ of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms…

Mathematical Physics · Physics 2022-03-09 Gandalf Lechner , Charley Scotford

For a new class of topological vector spaces, namely $\kappa $-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a $\kappa…

Functional Analysis · Mathematics 2007-05-23 S. V. Ludkovsky , J. C. Ferrando

This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…

Quantum Algebra · Mathematics 2007-05-23 Michael Penkava , Pol Vanhaecke

(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…

Logic · Mathematics 2013-05-23 Tarek Sayed Ahmed