On The Projective Classification of the Modules of Differential Operators on ℝm

2001 ◽  
pp. 123-129 ◽  
Author(s):  
Pierre B. A. Lecomte
Keyword(s):  
Differential Operators ◽  
Modules Of Differential Operators

Differential operators on the supercircle S1|2 and symbol map

2016 ◽  
Vol 14 (01) ◽  
pp. 1750002
Author(s):  
Raouafi Hamza ◽  
Zeineb Selmi ◽  
Jamel Boujelben
Keyword(s):  
Vector Fields ◽  
Differential Operators ◽  
Lie Superalgebra ◽  
Linear Differential Operators ◽  
Classical Setting ◽  
Modules Of Differential Operators ◽  
Linear Differential ◽  
Standard Contact ◽  
Funct Anal

We consider the supercircle [Formula: see text] equipped with the standard contact structure. The conformal Lie superalgebra [Formula: see text] acts on [Formula: see text] as the Lie superalgebra of contact vector fields; it contains the M[Formula: see text]bius superalgebra [Formula: see text]. We study the space of linear differential operators on weighted densities as a module over [Formula: see text]. We introduce the canonical isomorphism between this space and the corresponding space of symbols. This result allows us to give, in contrast to the classical setting, a classification of the [Formula: see text]-modules [Formula: see text] of linear differential operators of order [Formula: see text] acting on the superspaces of weighted densities. This work is the simplest superization of a result by Gargoubi and Ovsienko [Modules of differential operators on the real line, Funct. Anal. Appl. 35(1) (2001) 13–18.]

Differential operators on the weighted densities on the supercircle S1|1

2015 ◽  
Vol 52 (4) ◽  
pp. 477-503
Author(s):  
Nader Belghith ◽  
Mabrouk Ben Ammar ◽  
Nizar Ben Fraj
Keyword(s):  
Vector Fields ◽  
Differential Operators ◽  
Lie Superalgebra ◽  
Linear Differential Operators ◽  
Classical Setting ◽  
Linear Differential

Over the (1, 1)-dimensional real supercircle, we consider the K(1)-modules Dλ,μk of linear differential operators of order k acting on the superspaces of weighted densities, where K(1) is the Lie superalgebra of contact vector fields. We give, in contrast to the classical setting, a classification of these modules. This work is the simplest superization of a result by Gargoubi and Ovsienko.

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