nLab brace algebra


Brace algebra involves higher-order operations related to the study of A A_\infty-algebras. There is a sequence of canonical functors

dendriform algebras –> brace algebras –> pre-Lie algebras

Hence, in some sense, brace algebras are intermediate between dendriform algebras and pre-Lie algebras.

There is also a notion of a symmetric brace algebra which has analogous role for L L_\infty-algebras instead of A A_\infty. They are related to post-Lie algebras.


Brace algebras

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    Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 91 (1988) 19–27. MR91a:18016

  • M. Gerstenkhaber, A. A.Voronov, Higher-order operations on the Hochschild complex, Funktsional. Anal. i Prilozhen. 29:1 (1995) 1–6, 96; translation in Funct. Anal. Appl. 29 (1995), no. 1, 1–5. MR96g:18006
  • Ezra Getzler, Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology, Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992) 65–78, Israel Math. Conf. Proc. 7, 1993 MR95c:19002
  • Marcelo Aguiar, Infinitesimal bialgebras, pre-Lie and dendriform algebras, [pdf]

Symmetric brace algebras

category: algebra

Created on May 26, 2023 at 08:07:06. See the history of this page for a list of all contributions to it.