Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 073, 26 pages      arXiv:0907.2584      https://doi.org/10.3842/SIGMA.2009.073

On Linear Differential Equations Involving a Para-Grassmann Variable

Toufik Mansour a and Matthias Schork b
a) Department of Mathematics, University of Haifa, 31905 Haifa, Israel
b) Camillo-Sitte-Weg 25, 60488 Frankfurt, Germany

Received May 01, 2009, in final form July 05, 2009; Published online July 15, 2009

Abstract
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to n-generalized Fibonacci numbers is established. Several other classes of differential equations (systems of first order, equations with variable coefficients, nonlinear equations) are also considered and the analogies or differences to the usual (''bosonic'') differential equations discussed.

Key words: para-Grassmann variables; linear differential equations.

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