Triple Systems, Generalized Cohomologies and Connection

Viktor Abramov, University of Tartu, Estonia

We propose an analog of Grassmann algebra with ternary commutation relations of generators and study the structure of this algebra. We construct a calculus of partial derivatives with respect to the generators of this algebra and construct the operators which can be viewed as analogs of supersymmetry operators. We also develop an analogue of exterior calculus by means of a graded $q$-differential algebra and introduce a noncommutative analog of the notion of connection.