scholarly journals Noncommutative differential calculus on the κ-Minkowski space

1995 ◽  
Vol 349 (1-2) ◽  
pp. 42-48 ◽  
Author(s):  
Andrzej Sitarz
Keyword(s):  
Minkowski Space ◽  
Differential Calculus ◽  
Noncommutative Differential Calculus

scholarly journals DIFFERENTIAL STRUCTURE ON κ-MINKOWSKI SPACE, AND κ-POINCARÉ ALGEBRA

2011 ◽  
Vol 26 (20) ◽  
pp. 3385-3402 ◽  
Author(s):  
STJEPAN MELJANAC ◽  
SAŠA KREŠIĆ-JURIĆ
Keyword(s):  
Power Series ◽  
Hopf Algebra ◽  
Minkowski Space ◽  
Differential Calculus ◽  
Weyl Algebra ◽  
Algebra Structure ◽  
Exterior Derivative ◽  
Lorentz Algebra ◽  
Poincaré Algebra ◽  
Formal Power

We construct realizations of the generators of the κ-Minkowski space and κ-Poincaré algebra as formal power series in the h-adic extension of the Weyl algebra. The Hopf algebra structure of the κ-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on κ-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the κ-Minkowski space.

CARTAN CALCULUS OF Z3-GRADED DIFFERENTIAL CALCULUS ON THE QUANTUM PLANE

2012 ◽  
Vol 09 (05) ◽  
pp. 1250040
Author(s):  
ERDOĜAN MEHMET ÖZKAN
Keyword(s):  
Differential Calculus ◽  
Quantum Plane ◽  
Lie Derivatives ◽  
Noncommutative Differential Calculus

To give a Z3-graded Cartan calculus on the extended quantum plane, the noncommutative differential calculus on the extended quantum plane is extended by introducing inner derivations and Lie derivatives.

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