Symmetrization of brace algebra

@inProceedings{Daily2006,
abstract = {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 $\bigoplus _\{k\ge 1\}\operatorname\{Hom\}(V^\{\otimes k\},V)$ coincides with the natural symmetric brace structure on $\bigoplus _\{k\ge 1\}\operatorname\{Hom\}(V^\{\otimes k\},V)^\{as\}$, the direct sum of spaces of antisymmetric maps $V^\{\otimes k\}\rightarrow V$.},
author = {Daily, Marilyn, Lada, Tom},
booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
location = {Palermo},
pages = {[75]-86},
publisher = {Circolo Matematico di Palermo},
title = {Symmetrization of brace algebra},
url = {http://eudml.org/doc/221515},
year = {2006},
}

TY - CLSWK
AU - Daily, Marilyn
AU - Lada, Tom
TI - Symmetrization of brace algebra
T2 - Proceedings of the 25th Winter School "Geometry and Physics"
PY - 2006
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [75]
EP - 86
AB - 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 $\bigoplus _{k\ge 1}\operatorname{Hom}(V^{\otimes k},V)$ coincides with the natural symmetric brace structure on $\bigoplus _{k\ge 1}\operatorname{Hom}(V^{\otimes k},V)^{as}$, the direct sum of spaces of antisymmetric maps $V^{\otimes k}\rightarrow V$.
UR - http://eudml.org/doc/221515
ER -