Answer by Tom Goodwillie for Tensor product of irreducible representations of...
Here is an example in which $A$ is freely generated by two elements $x,y$. Let $W$ be $\mathbb C^2$ with representation given by$$x(a_1,a_2)=(0,a_1)$$$$y(a_1,a_2)=(a_2,0).$$This is irreducible. Let $V$...
View ArticleAnswer by Benjamin Steinberg for Tensor product of irreducible...
By a famous theorem of R. Steinberg, STEINBERG, R. Complete sets of representations of algebras. PROC. Am. Math. Soc. 13 (1962), 746-747, if $V$ is a faithful representation for a monoid $M$, then...
View ArticleTensor product of irreducible representations of an algebra
Let $A$ be an associative algebra over $\mathbb{C}$ with irreducible finite-dimensional representations on $V$ and $W$. Then is the tensor product of representations on $V \otimes W$ semi-simple?The...
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