From Hopf Algebra to Braided L∞-Algebra

Grewcoe, Clay James; Jonke, Larisa; Kodžoman, Toni; Manolakos, G.

doi:10.3390/universe8040222

Cited by 4 publications

(1 citation statement)

References 36 publications

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“…In this work a braided version of the Einstein-Cartan-Palatini gravitational theory is formulated. Moreover, in [83], braided L ∞ algebras are produced making use of the Drinfel'd twist of the graded Hopf algebra, which, in presence of a compatible codifferential, consists an alternative form of the underlying L ∞ algebra.…”

Section: Introductionmentioning

confidence: 99%

A Matrix Model of Four-Dimensional Noncommutative Gravity

et al. 2022

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In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, of the well-established formulation of gauge theories on them. Making use of a covariant four-dimensional fuzzy space, we formulate the gauge theory with an extended gauge group due to noncommutativity. In turn, in order to decrease the amount of symmetry we employ a symmetry breaking and result with an action which describes a theory that is a minimal noncommutative extension of the original.

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Section: Introductionmentioning

confidence: 99%

A Matrix Model of Four-Dimensional Noncommutative Gravity

et al. 2022

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Braided symmetries in noncommutative field theory

Giotopoulos

Szabo

2022

J. Phys. A: Math. Theor.

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We give a pedagogical introduction to $L_\infty$-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective field theories in string theory. We review recent developments which formulate field theories with braided gauge symmetries as a new means of overcoming several obstacles in the standard noncommutative theories, such as the restrictions on gauge algebras and matter fields. These theories can be constructed by using techniques from Drinfel'd twist deformation theory, which we review in some detail, and their symmetries and dynamics are controlled by a new homotopy algebraic structure called a `braided $L_\infty$-algebra'. We expand and elaborate on several novel theoretical issues surrounding these constructions, and present three new explicit examples: the standard noncommutative scalar field theory (regarded as a braided field theory), a braided version of $BF$ theory in arbitrary dimensions (regarded as a higher gauge theory), and a new braided version of noncommutative Yang--Mills theory for arbitrary gauge algebras.

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Noncommutative double geometry

Kodžoman,

Lescano

2024

Phys. Rev. D

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We construct noncommutative theories with the Moyal-Weyl product in the double field theory (DFT) framework. We deform the infinitesimal generalized diffeomorphisms and the Leibniz rule in a consistent way. The prescription requires a generalized star metric, which can be thought of as the fundamental double metric, in order to construct the action. Finally we use the generalized scalar field dynamics and the generalized scalar field-perfect fluid correspondence to construct the generalized energy-momentum tensor of a perfect fluid in the noncommutative double geometry. The present formalism paves the way to the study of string cosmologies scenarios including the Moyal-Weyl product in a T-duality invariant way. Published by the American Physical Society 2024

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From Hopf Algebra to Braided L∞-Algebra

Cited by 4 publications

References 36 publications

A Matrix Model of Four-Dimensional Noncommutative Gravity

A Matrix Model of Four-Dimensional Noncommutative Gravity

Braided symmetries in noncommutative field theory

Noncommutative double geometry

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