The authors define averaging groups and averaging Hopf algebras, show how averaging groups induce racks and disemigroups, and explicitly construct the free averaging group on a set.
Aguiar, Pre-Poisson algebras, Lett
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Averaging operators on groups and Hopf algebras
The authors define averaging groups and averaging Hopf algebras, show how averaging groups induce racks and disemigroups, and explicitly construct the free averaging group on a set.