Abstract
We consider a method that allows to construct the 3-Lie algebra if we have a Lie algebra equipped with an analogue of the notion of trace. At the same time, it is well known that, based on a Lie algebra, we can construct the Weil algebra, which is a universal model for connection and curvature. In this paper, we propose an answer to the question of how one could extend the construction of the Weil algebra from a Lie algebra to the induced 3-Lie algebra. To this end, in addition to universal connection and curvature, we introduce new elements and extend the action of the differential of Weil algebra to these new elements with the help of structure constants of 3-Lie algebra. Since one of the most important applications of Weil algebra in a field theory is the construction of B.R.S. algebra, we propose an analogue of B.R.S. algebra constructed by means of a 3-Lie algebra.
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