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On graded polynomial identities of $sl_{2}(F)$ over a finite field (1311.3904v14)
Published 15 Nov 2013 in math.RA
Abstract: Let $F$ be a finite field of $char F > 3$ and $sl_{2}(F)$ be the Lie algebra of traceless $2\times 2$ matrices over $F$. This paper aims for the following goals: Find a basis for the $\mathbb{Z}{2}$-graded identities of $sl{2}(F)$; Find a basis for the $\mathbb{Z}{3}$-graded identities of $sl{2}(F)$ when $F$ contains a primitive 3rd root of one; Find a basis for the $\mathbb{Z}{2}\times \mathbb{Z}{2}$-graded identities of $sl_{2}(F)$.