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An algebra whose (left) multiplications are derivations is referred to as a (left) Leibniz algebra (or Loday algebra). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Jorg Feldvoss: https://arxiv.org/abs/1802.07219.

An algebra whose (left) multiplications are derivations is referred to as a (left) Leibniz algebra (or Loday algebra). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Joerg Feldvoss: https://arxiv.org/abs/1802.07219.

An algebra whose (left) multiplications are derivations is referred to as (left) Lebniz algebra (or Loday algebra). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Jorg Feldvoss: https://arxiv.org/abs/1802.07219.

An algebra whose (left) multiplications are derivations is referred to as a (left) Leibniz algebra (or Loday algebra). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Jorg Feldvoss: https://arxiv.org/abs/1802.07219.

An algebra whose (left) multiplications are derivations is referred to as (left) \emph{Lebniz algebra} (or \emph{ Loday algebra}). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Jorg Feldvoss: https://arxiv.org/abs/1802.07219.

An algebra whose (left) multiplications are derivations is referred to as (left) Lebniz algebra (or Loday algebra). There is a large literature about this class of non-associative algebras. See e.g. the following survey by Jorg Feldvoss: https://arxiv.org/abs/1802.07219.