Weil Algebra, 3-Lie Algebra and B.R.S. Algebra

Abstract

We consider the 3-Lie algebra induced by a Lie algebra with the help of an analog of a trace. We propose the extension of the Weil algebra of a Lie algebra to the Weil algebra of induced 3-Lie algebra by introducing in addition to an analog of connection and its curvature new elements and defining their differential by means of structure constants of 3-Lie algebra. We also propose a new approach to the universal B.R.S. algebra based on the quantum triple Nambu bracket.

10 pages, will appear in the Proceedings of International Conference on Stochastic Processes and Algebraic Structures (SPAS2017)