Symmetric Brace Algebras

Details Symmetric Brace Algebras Symmetric Brace Algebras

2003-07-03

arxiv.org/abs/math/0307054v3

Mathematics

Quantum Algebra

19 pages; two new sections added: "Equivalence between symmetric brace algebras and pre-Lie algebras" and "Transfers of strong

Scientific paper

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to $L_{\infty}$-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the $L_{\infty}$-algebras that result from a particular gauge theory for massless particles of high spin.

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