Algebra of differential forms with exterior differential $d^3=0$ in dimension one

Details Algebra of differential forms with exterior differential $d^3=0$ in dimension one Algebra of differential forms with exterior differential $d^3=0$ in dimension one

2000-01-29

arxiv.org/abs/math-ph/0001041v1

Physics

Mathematical Physics

9 pages, LaTeX. This paper is based on the talk given by the first Author at the Sixth International Wigner Symposium, Istanbu

Scientific paper

In this work, we construct the algebra of differential forms with the cube of exterior differential equal to zero on one-dimensional space. We prove that this algebra is a graded q-differential algebra where q is a cubic root of unity. Since the square of differential is not equal to zero the algebra of differential forms is generated not only by the first order differential but also by the second order differential of a coordinate. We study the bimodule generated by this second order differential, and show that its structure is similar to the structure of bimodule generated by the first order differential in the case of anyonic line.

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