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

TL;DR

This paper extends the concept of Weil algebra from Lie algebras to 3-Lie algebras using trace analogs and introduces a novel approach to the B.R.S. algebra via the quantum triple Nambu bracket.

Contribution

It develops a framework for Weil algebra and B.R.S. algebra in the context of 3-Lie algebras, expanding algebraic structures in gauge theories.

Findings

Extended Weil algebra to 3-Lie algebra using structure constants.

Proposed a new approach to B.R.S. algebra with quantum triple Nambu bracket.

Defined differential structures for the induced 3-Lie 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.