I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2005, VOLUME 11, NUMBER 3, PAGES 57-78
Zinbiel algebras under -commutator
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An algebra with the identity
is called Zinbiel.
For example, under
multiplication is Zinbiel.
Let be a -commutator, where
We prove that for any Zinbiel algebra the corresponding algebra
satisfies the identities
We find basic identities for -Zinbiel algebras and
prove that they form varieties equivalent to the variety of Zinbiel
algebras if .
Last modified: September 14, 2005