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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 coincides with the natural symmetric brace structure on , the direct sum of spaces of antisymmetric maps .
Daily, Marilyn, and Lada, Tom. "Symmetrization of brace algebra." Proceedings of the 25th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2006. [75]-86. <http://eudml.org/doc/221515>.
@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 -