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For the sake of simplicity, I will work over the complex numbers. Let $A$ be a finitely generated algebra and $G$ any finite group of algebra automorphisms. Then, by Noether's Theorem, $A^G$ is also a …

I have exchanged e-mail with some specialists on invariant theory and affine algebraic geometry, and here is a summary of what I learned. For the sake of simplicity (although this is by no means neces …

Let $k$ be a field, $P_n$ the polynomial algebra in $n$ indeterminates, and $G<\operatorname{GL}_n$ a finite group whose order is coprime to the characteristic of $k$, and that acts on $P_n$ by algebr …

Major Edit I will reformulate my question signicantly, given Anton Geraschenko's comment. The old version of the question is bellow. For simplicity, my base field is $\mathbb{C}$. If $G<\operatorname{ …

For finitely generated domains over a base field $k$ of characteristic 0, we have that if $A$ is regular, then both $Der_k \, A$ and the module of Kähler differentials are finitely generated projectiv …

The class of Jordan algebras are the most important class of algebras in this direction. They are defined by the two identities, (commutativity): $xy=yx$, (Jordan identity): $(xy)(xx)=x(y(xx))$. They …

Expanding the last entry on noncommutative transcendence degrees: When your algebra $A$ is prime Goldie (such as Noetherian domains) there are two recent analogues of noncommutative transcendence degr …