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So, I've been very interested recently with the developements of the (now mathematically precise) theory of Coulomb branches - in particular because of its recent applications on representation theory …

As it was shown by Malcev, unlike the commutative case, in which every domain can be embedded in a field, there are noncommutative domains that can't be embedded in a division ring. For noncommutative …

My question os motivated, naturally, by the problem of classifying symplectic reflection algebras up to Morita equivalence (a classical reference for rational Cherednik algebras is Y. Berest, P. Eting …

We will work over $\mathbb{C}$. Remember that a finite subgroup $G$ of $\operatorname{GL}_n(\mathbb{C})$ is called a complex reflection group if it is generated by complex reflections $r$, which are l …

In his seminal paper, Some open problems on three-dimensional graded domains, M. Artin proposed a very small list of possible division rings of fractions that can appear as 'noncommutative function fi …

Let $\mathcal{L}$ be a first-order language, and $M$ and $N$ be two $\mathcal{L}$-structures. We say that $M$ and $N$ are elementarily equivalent (write $M \approx N$) if they satisfy the same first-o …

In his very influential book Infinite dimensional Lie algebras, which is still the main reference for Kac-Moody algebras, in section 0.4 of the introduction, Victor Kac discuss the problem of concrete …

It is almost two decades since the now classical books by McConnell and Robinson's [ Noncommutative Noetherian rings. With the cooperation of L. W. Small. Revised edition. Graduate Studies in Mathema …

A modern approach to derived functors, that has been shown to be useful in a number of different circunstances is that of a derived category (see the book by Yakutieli, for example, here). However, it …

Suppose $\mathsf{k}$ is an algebraically closed field of zero characteristic. Chevalley-Shephard-Todd (C-S-T) Theorem in one of its equivalent versions is the following result: (C-S-T): Let $G$ be a f …

$\DeclareMathOperator\GK{GK}$Let $k$ be the base field. The Gelfand-Kirillov dimension was introduced by Gelfand and Kirillov in their seminal paper on the Gelfand-Kirillov conjecture. A very famous p …

For english references: An history of mathematics book, but extremely well written and mathematically sophisticated, with tons of references (that might be useuful) that adress all such things is G. …

Let $\mathbb{k}$ be an algebraically closed field of positive characteristic, $X$ an affine smooth variety over it. Then the ring of crystalline differential operators on $X$ is generated by $\mathcal …

This question is a follow up to my previous question on rings of crystaline differential operators, to which I refer for the adequate definitions. First, let's consider the case of an algebraically cl …

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 …