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- W3217232616 abstract "Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${rm Aut}_{rm Alg} (A)$ of $A$ is isomorphic to the group $U bigl( G(a (A)^{rm o} ) bigl)$ of all invertible group-like elements of the finite dual $a (A)^{rm o}$. For a group $G$, all $G$-gradings on $A$ are explicitly described and classified: the set of isomorphisms classes of all $G$-gradings on $A$ is in bijection with the quotient set $ {rm Hom}_{rm BiAlg} , bigl( a (A) , , k[G] bigl)/approx$ of all bialgebra maps $a (A) , to k[G]$, via the equivalence relation implemented by the conjugation with an invertible group-like element of $a (A)^{rm o}$." @default.
- W3217232616 created "2021-12-06" @default.
- W3217232616 creator A5056470367 @default.
- W3217232616 date "2021-11-18" @default.
- W3217232616 modified "2023-10-10" @default.
- W3217232616 title "The Automorphisms Group and the Classification of Gradings of Finite Dimensional Associative Algebras" @default.
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- W3217232616 doi "https://doi.org/10.1007/s00025-021-01509-z" @default.
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