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On multilinear polynomial identities for $2\times2$ matrices in characteristic $2$
Let $K$ be an infinite field of characteristic $2$. It is well known that the Lie algebra $\mathfrak{gl}_2(K)=M_2(K)^{(-)}$ of all $2\times 2$ matrices does not admit a finite basis of polynomial identities. Similarly, the finite basis problem for the associative algebra $M_2(K)$ remains open. In th
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