Non-commutative gauge symmetry from strong homotopy algebras

Abstract

We explicitly construct an L${}_{\infty }$ algebra that defines U${}_{\star }(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L${}_{\infty }$ modules. Some possibilities for including P${}_{\infty }$ algebras are also discussed.

21 pages; published version

References in corpus (8)

• T-duality and closed string non-commutative (doubled) geometry
• Star products made (somewhat) easier
• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Gauge theories on quantum spaces
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Braided Symmetries in Noncommutative Field Theory
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories

Cited by in corpus (1)

• Poisson electrodynamics on $\kappa$-Minkowski space-time