Algebraic Analysis of Differential Equations
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URI (for links/citations):
https://elib.sfu-kras.ru/handle/2311/827Author:
Osetrova, Tatyana A.
Tarkhanov, Nikolai
(Tatyana A.Osetrova: Institute of Mathematics
Siberian Federal University Svobodny 79, Krasnoyarsk, 660041, Russia, e-mail: osetrova@lan.krasu.ru; Nikolai Tarkhanovy: Institut fur Mathematik Universitat Potsdam
Am Neuen Palais 10, 14469 Potsdam, Germany, e-mail: tarkhanov@math.uni-potsdam.de)
Date:
2008-11Abstract:
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.