Braided L -algebras, braided field theory and noncommutative gravity

Marija Dimitrijević Ćirić, Grigorios Giotopoulos*, Voja Radovanović, Richard J. Szabo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
13 Downloads (Pure)


We define a new homotopy algebraic structure, that we call a braided L-algebra, and use it to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act on the solutions of the field equations. We use Drinfel’d twist deformation quantization techniques to generate new noncommutative deformations of classical field theories with braided gauge symmetries, which we compare to the more conventional theories with star-gauge symmetries. We apply our formalism to introduce a braided version of general relativity without matter fields in the Einstein–Cartan–Palatini formalism. In the limit of vanishing deformation parameter, the braided theory of noncommutative gravity reduces to classical gravity without any extensions.

Original languageEnglish
Article number148
JournalLetters in Mathematical Physics
Issue number6
Early online date7 Dec 2021
Publication statusPublished - Dec 2021


  • Drinfeld twist
  • L-algebra
  • Noncommutative gravity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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