On the pre-commutative envelopes of commutative algebras
arXiv:2405.03531 · doi:10.1142/s0219498826500088
Abstract
We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional algebras, the nilpotency condition is necessary for a commutative algebra to have a pre-commutative envelope.
13 pages