An introduction to some novel applications of Lie algebra cohomology and physics
J. A. de Azcarraga, J. M. Izquierdo, J. C. Perez Bueno
TL;DR
This paper introduces Lie algebra cohomology and explores its recent applications in mathematics and physics, including differential geometry, higher order structures, and generalized Poisson structures, providing a comprehensive overview of novel theoretical developments.
Contribution
It offers a self-contained introduction to Lie algebra cohomology and presents new applications in physics and mathematics, emphasizing higher order structures and their implications.
Findings
Development of higher order cocycles and Lie algebra structures
Application of cohomology to generalized Poisson structures
Insights into effective WZW actions and coset spaces
Abstract
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra cohomology: a brief introduction 4. Symmetric polynomials and higher order cocycles 5. Higher order simple and SH Lie algebras 6. Higher order generalized Poisson structures 7. Relative cohomology, coset spaces and effective WZW actions
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology