×

zbMATH — the first resource for mathematics

Symmetrization of brace algebras. (English) Zbl 1162.18302
Čadek, Martin (ed.), The proceedings of the 25th winter school “Geometry and physics”, Srní, Czech Republic, January 15–22, 2006. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 79, 75-86 (2006).
Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on \(\bigoplus_{k\geq 1}\operatorname{Hom}(V^{\otimes k},V)\) coincides with the natural symmetric brace structure on \(\bigoplus_{k\geq 1}\operatorname{Hom}(V^{\otimes k},V)^{as}\), the direct sum of spaces of antisymmetric maps \(V^{\otimes k}\to V\).
For the entire collection see [Zbl 1103.53001].

MSC:
18D50 Operads (MSC2010)
55S20 Secondary and higher cohomology operations in algebraic topology
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
PDF BibTeX XML Cite
Full Text: arXiv