e-mail: nadegda@ut.ee

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

**Abstract**

My talk is based on the paper, whith appear in Turkish Jourmal of Physics.
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
this algebra is 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 second
order differential. We study the bimodule generated by this second order
differential, and show its structure is similar to the structure of bimodule
generated by the first order

differential in the case of the anyonic line.