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Keywords:
quasigroup; $3$-sorted quasigroup; homotopy; isotopy; quadratic identity; gemini identity; coherent identity; variety closed under isotopy (homotopy)
quasigroup; $3$-sorted quasigroup; homotopy; isotopy; quadratic identity; gemini identity; coherent identity; variety closed under isotopy (homotopy)
Summary:
According to S. Krstić, there are only four quadratic varieties which are closed under isotopy. We give a simple procedure generating quadratic identities and deciding which of the four varieties they define. There are about 37000 such identities with up to five variables.
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