Brackets by any other name

DOI10.3934/jgm.2021014zbMath1494.16001arXiv2105.09724OpenAlexW3185558787MaRDI QIDQ2065153

James D. Stasheff

Publication date: 7 January 2022

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.09724

zbMATH Keywords

deformation theoryproductsLiebracesbracketshigher homotopy algebras and operationsLeibniz and Filippov algebras

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Poisson manifolds; Poisson groupoids and algebroids (53D17) Graded Lie (super)algebras (17B70) History of associative rings and algebras (16-03) Massey products (55S30) Homotopical algebra, Quillen model categories, derivators (18N40) Whitehead products and generalizations (55Q15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher Toda brackets and Massey products
• From Poisson algebras to Gerstenhaber algebras
• Lie-Massey brackets and \(n\)-homotopically multiplicative maps of differential graded Lie algebras
• The intrinsic bracket on the deformation complex of an associative algebra
• Derived brackets
• Double Lie algebroids and representations up to homotopy
• Leibniz gauge theories and infinity structures
• Symmetric brace algebras
• The Noether theorems. Invariance and conservation laws in the twentieth century. Transl. from the French by Bertram E. Schwarzbach
• The Lie algebra structure of tangent cohomology and deformation theory
• Deformation theory and quantization. I: Deformations of symplectic structures
• Deformation theory and quantization. II: Physical applications
• Introduction to sh Lie algebras for physicists
• On foundation of the generalized Nambu mechanics
• A noncommutative version of Lie algebras: Leibniz algebras
• Higher-order simple Lie algebras
• Manin triples for Lie bialgebroids
• On some generalizations of Batalin-Vilkovisky algebras
• sh-Lie algebras induced by gauge transformations
• Nambu-Dirac structures for Lie algebroids
• On Lie \(k\)-algebras
• From Schouten to Mackenzie: notes on brackets
• The embedding tensor, Leibniz-Loday algebras, and their higher gauge theories
• Tensor hierarchies and Leibniz algebras
• Higher Whitehead products in moment-angle complexes and substitution of simplicial complexes
• New perspectives on the BRST-algebraic structure of string theory
• The cohomology structure of an associative ring
• Higher order Whitehead products
• The geometry of iterated loop spaces
• Action of the symmetric group on the free LAnKe: a CataLAnKe theorem
• On adding relations to homotopy groups
• Note on the Whitehead product
• Missed opportunities
• Compositional Methods in Homotopy Groups of Spheres. (AM-49)
• HIGHER WHITEHEAD PRODUCTS
• n-ary algebras: a review with applications
• ON THE HOMOLOGY THEORY OF FIBRE SPACES
• Invariant variation problems
• Extensions of Lie-Rinehart algebras and the Chern-Weil construction
• Generalized Hamiltonian Dynamics
• Strongly homotopy lie algebras
• algebras and field theory
• Homotopy Associativity of H-Spaces. I
• A Connection Between the Whitehead and the Pontryagin Product
• Conditional Invariants
• Multibraces on the Hochschild space