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- W2796448562 abstract "Let $k$ be a field, $A$ a finitely generated associative $k$-algebra and $operatorname{Rep}_A[n]$ the functor $operatorname{Fields}_kto operatorname{Sets}$, which sends a field $K$ containing $k$ to the set of isomorphism classes of representations of $A_K$ of dimension at most $n$. We study the asymptotic behavior of the essential dimension of this functor, i.e., the function $r_A(n) := operatorname{ed}_k(operatorname{Rep}_A[n])$, as $ntoinfty$. In particular, we show that the rate of growth of $r_A(n)$ determines the representation type of $A$. That is, $r_A(n)$ is bounded from above if $A$ is of finite representation type, grows linearly if $A$ is of tame representation type and grows quadratically if A is of wild representation type. Moreover, $r_A(n)$ is a finer invariant of A, which allows us to distinguish among algebras of the same representation type." @default.
- W2796448562 created "2018-04-13" @default.
- W2796448562 creator A5059505346 @default.
- W2796448562 date "2018-04-02" @default.
- W2796448562 modified "2023-09-27" @default.
- W2796448562 title "New numerical invariants for representations of algebras" @default.
- W2796448562 hasPublicationYear "2018" @default.
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