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Introduction to sh Lie algebras for physicists
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Closed string field theory leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures. It also appeared in work on higher spin particles \cite{BBvD}. Representation theoretic analogs arose in the mathematical analysis of the Batalin-Fradkin-Vilkovisky approach to constrained Hamiltonians. A major goal of this paper is to see the relevant formulas, especially in closed string field theory, as a generalization of those for a differential graded Lie algebra, hopefully describing the mathematical essentials in terms accessible to {\it physicists}.
Forward citations
Cited by 12 Pith papers
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$L_\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings
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Covariant phase space and $L_\infty$ algebras
A covariant phase space symplectic form is constructed for any L∞ Lagrangian field theory using a 'sigmoid' operator, and is verified in scalar, Yang-Mills, general relativity, and p-adic string examples.
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The Double Copy of Maximal Supersymmetry in $D=4$
N=8 supergravity to cubic order is realized as the off-shell double copy of N=4 super Yang-Mills, with N=8 supersymmetry and SU(8) R-symmetry emerging from the two gauge factors.
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Universal quadratic field equations via homotopy algebras
The bar-cobar construction turns the equations of motion of any homotopy-algebra gauge theory into universal quadratic Maurer-Cartan equations, with solutions equivalent to the original theory.
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Conserved charges and $L_\infty$ algebras
A formula for conserved charges expressed solely via L_infinity algebra data for arbitrary Lagrangian theories, shown to recover the Brown-York surface charge in GR.
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Explicit class of finite-dimensional polynomial algebras with Wronskians over $\mathbb{R}^d$ as $N$-ary Lie brackets: beyond $\mathfrak{sl}(2)$
Explicit classification of all finite-dimensional polynomial SH-Lie algebras over R^d or C^d using complete generalized Wronskians of order k as N-ary brackets, together with a factorization formula for the associated...
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refining charge quantization via a homotopy type A yields swampland-like constraints ruling out noncompact gauge groups and non-nilpotent one-form Lie algebras, and requires A to be contractible for quantum gravity theories.
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Gauged Extended Field Theory and Generalised Cartan Geometry
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Quantum flux operators in the fermionic theory and their supersymmetric extension
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Super-$\mathrm{Lie}_\infty$ T-Duality and M-Theory
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Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.
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Towards an M5-Brane Model II: Metric String Structures
Adjusted Weil algebras for skeletal and loop models of the string Lie 2-algebra and their metric extensions yield local metric string structure connections whose gauge transformations close without fake flatness, matc...
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