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For questions on modules over rings.

3 votes
0 answers
98 views

Dimension of hom spaces between indecomposable modules

$X$ and $Y$ are equivalent to finite direct sums of (not necessarily projective) indecomposable modules. … In particular, are there sets of modules $\{J_a\}, \{J_a^*\}$ "dual" to the set of indecomposable modules $\{I_a\}$ in the sense that $$dim_k Hom_C(I_a, J_b) = \delta_{ab} = dim_k Hom_C(J_a^*, I_b)? …
1 vote
1 answer
392 views

Making use of extra symmetries; more examples?

seems exclusive for topological compact groups.. therefore the questions: Questions What else algebra $A$ has an element that serves as the projection to a given isotypic component for any of its left modules