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$\begingroup$

I am familiar with the direct sum of sets, $\oplus$.

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    In what context? In some contexts, it means tensor product.2011-04-07
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    More generally, this list can be useful: http://en.wikipedia.org/wiki/List_of_mathematical_symbols2011-04-07
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    The direct sum of sets?!?2011-04-07
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    The $\otimes$ symbol usually means 'some multiplicative binary operation', which may differ depending on context.2013-12-01

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The $\otimes$ symbol is used for the tensor product.