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Sep 3, 2020 at 2:56 comment added Benjamin Steinberg The result mentioned in the answer to this question mathoverflow.net/questions/369932/… certainly covers the case of HxH. The proof given there will handle the general case. It all boils down to the tensor product over k of matrix algebras over k if a matrix algebra over k.
Sep 3, 2020 at 1:46 comment added Benjamin Steinberg If k splits groups G,H then it splits $G\times H$. More generally the tensor product of split finite dimensional algebras is split.
Sep 2, 2020 at 23:44 history asked Stein Chen CC BY-SA 4.0