Invariant Differential Calculus on a Deformation of the Weyl-Heisenberg Algebra

1995 ◽  
pp. 37-49
Author(s):  
J. Bertrand ◽  
M. Irac-Astaud
Keyword(s):  
Differential Calculus ◽  
Heisenberg Algebra ◽  
Invariant Differential

scholarly journals DIFFERENTIAL CALCULUS ON A THREE-PARAMETER OSCILLATOR ALGEBRA

1996 ◽  
Vol 08 (08) ◽  
pp. 1083-1090 ◽  
Author(s):  
MICHÈLE IRAC-ASTAUD
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Differential Calculus ◽  
Heisenberg Algebra ◽  
Invariance Group ◽  
Oscillator Algebra ◽  
Special Case

Two differential calculi are developed on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a ten-generator Hopf algebra. We discuss the special case where it reduces to a deformation of the invariance group of the Weyl-Heisenberg algebra for which we prove the existence of a constraint between the values of the parameters.

scholarly journals Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Francesco Toppan ◽  
Mauricio Valenzuela
Keyword(s):  
Differential Operators ◽  
Similarity Transformation ◽  
Heisenberg Algebra ◽  
Dynamical Symmetries ◽  
First Order ◽  
Enveloping Algebra ◽  
Higher Spin ◽  
Invariant Differential ◽  
Order Invariant ◽  
Schrödinger Algebra

The dynamical symmetries of 1+1-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial de Alfaro-Fubini-Furlan, DFF, term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the sl(2)⊕u(1) invariance of the Calogero Conformal Mechanics, an osp2∣2 invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher-spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable.

scholarly journals THE TWO-PARAMETRIC EXTENSION OF h DEFORMATION OF GL(2), AND THE DIFFERENTIAL CALCULUS ON ITS QUANTUM PLANE

1993 ◽  
Vol 08 (27) ◽  
pp. 2607-2613 ◽  
Author(s):  
AMIR AGHAMOHAMMADI
Keyword(s):  
Quantum Group ◽  
Differential Calculus ◽  
Heisenberg Algebra ◽  
Quantum Plane ◽  
Two Dimensional

We present an alternative two-parametric deformation GL (2)h,h′, and construct differential calculus on the quantum plane on which this quantum group acts. We also give a new deformation of the two-dimensional Heisenberg algebra.

Bialgebra structures on the Heisenberg algebra

1989 ◽  
Vol 75 (1) ◽  
pp. 315-321
Author(s):  
Michel Cahen ◽  
Christian Ohn
Keyword(s):  
Heisenberg Algebra

EXPLORING POSSIBLE CAUSES OF POOR PERFORMANCE BY HIGH SCHOOL STUDENTS IN DIFFERENTIAL CALCULUS

2017 ◽  
Vol 73 (8) ◽  
Author(s):  
Deonarain Brijlall ◽  
Reuben Bafana Dlamini ◽  
Zingiswa Jojo
Keyword(s):  
High School ◽  
High School Students ◽  
Differential Calculus ◽  
Poor Performance ◽  
School Students

scholarly journals Noncommutative differential calculus for Moyal subalgebras

2006 ◽  
Vol 56 (4) ◽  
pp. 611-622 ◽  
Author(s):  
G. Marmo ◽  
P. Vitale ◽  
A. Zampini
Keyword(s):  
Differential Calculus ◽  
Noncommutative Differential Calculus

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

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