Geodesic
Algebraic Analysis of Differential Equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 391-398.

Voir la notice de l'article provenant de la source Math-Net.Ru

Given any algebra over a field with a finite number of generators, we define a first order partial differential operator acting on functions taking their values in the algebra. While being not canonical, the construction is fairly natural. We call this differential operator Dirac operator related to the algebra, and show some examples. Conversely, to each homogeneous first order differential operator one assigns an algebra which absorbs formal properties of the operator.
Keywords: normed algebras. 
@article{JSFU_2008_1_4_a3,
     author = {Tatyana A. Osetrova and Nikolai N. Tarkhanov},
     title = {Algebraic {Analysis} of {Differential} {Equations}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {391--398},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a3/}
}
TY  - JOUR
AU  - Tatyana A. Osetrova
AU  - Nikolai N. Tarkhanov
TI  - Algebraic Analysis of Differential Equations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 391
EP  - 398
VL  - 1
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a3/
LA  - en
ID  - JSFU_2008_1_4_a3
ER  - 
%0 Journal Article
%A Tatyana A. Osetrova
%A Nikolai N. Tarkhanov
%T Algebraic Analysis of Differential Equations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 391-398
%V 1
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a3/
%G en
%F JSFU_2008_1_4_a3
Tatyana A. Osetrova; Nikolai N. Tarkhanov. Algebraic Analysis of Differential Equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 391-398. http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a3/

[1] P. J. Olver, Equivalence, Invariants, and Symmetry, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl