Differential graded Lie algebras and formal deformation theory

2009 ◽  
pp. 785-810 ◽  
Author(s):  
Marco Manetti
Keyword(s):  
Lie Algebras ◽  
Deformation Theory ◽  
Graded Lie Algebras ◽  
Formal Deformation ◽  
Formal Deformation Theory ◽  
Differential Graded Lie Algebras

Complete Differential Graded Lie Algebras

2020 ◽  
pp. 71-91
Author(s):  
Urtzi Buijs ◽  
Yves Félix ◽  
Aniceto Murillo ◽  
Daniel Tanré
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Differential Graded Lie Algebras

scholarly journals Duality Hierarchies and Differential Graded Lie Algebras

2021 ◽  
Vol 382 (1) ◽  
pp. 277-315
Author(s):  
Roberto Bonezzi ◽  
Olaf Hohm
Keyword(s):  
Lie Algebras ◽  
Scalar Fields ◽  
Vector Spaces ◽  
Graded Lie Algebras ◽  
Yang Mills ◽  
Leibniz Algebras ◽  
Duality Relations ◽  
Graded Lie Algebra ◽  
Differential Graded Lie Algebra ◽  
Differential Graded Lie Algebras

AbstractThe gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by ‘infinity-enhanced Leibniz algebras’ defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. We use this observation to streamline the construction of general tensor hierarchies, and we formulate dynamics in terms of a hierarchy of first-order duality relations, including scalar fields with a potential.

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