Related papers: Noncommutative Noether's problem is almost equival…

The inverse Galois problem asks whether any finite group can be realised as the Galois group of a Galois extension of the rationals. This problem and its refinements have stimulated a large amount of research in number theory and algebraic…

Let $k$ be algebraically closed field of characteristic zero, let $G$ be a commutative algebraic group over $k$ such that the linear part of $G$ is isomorphic to $\mathbb{G}_a$, and let $X$ be a closed subvariety of $G$. We show that the…

Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…

The classical Noether Normalization Lemma states that if $S$ is a finitely generated algebra over a field $k$, then there exist elements $x_1,\dots,x_n$ which are algebraically independent over $k$ such that $S$ is a finite module over…

The non-commutative analytic Toeplitz algebra is the weak operator topology closed algebra generated by the left regular representation of the free semigroup on $n$ generators. The structure theory of contractions in these algebras is…

Jackiw was undoubtedly the first to exhibit an example of a scalar field action which is not conformally invariant whereas its equation of motion is. This feature has recently been dubbed as a non-Noetherian conformal scalar field. The…

Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws.…

In this paper, first, we answer affirmatively an open problem which was presented in 2005 by professor Gudder on the sub-sequential effect algebras. That is, we prove that if $(E,0,1, \oplus, \circ)$ is a sequential effect algebra and $A$…

Let $\mathfrak F$ be a class of groups. A group $G$ is called $ca$-$\mathfrak F$-group if its every non-abelian chief factor is simple and $H/K \leftthreetimes C_G(H/K) \in \mathfrak F$ for every abelian chief factor $H/K$ of $G$. In this…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

Let $G$ be a nonabelian group, $A\subseteq G$ an abelian subgroup and $n\geqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into $A$ and $n$ disjoint commuting…

Let $R$ be a Dedekind domain, $G$ an affine flat $R$-group scheme, and $B$ a flat $R$-algebra on which $G$ acts. Let $A \to B^G$ be an $R$-algebra map. Assume that $A$ is Noetherian. We show that if the induced map $K\otimes A\to (K\otimes…

We show that some abstract results on propagation of fixed points for completely positive maps on $C^*$-algebras provide a natural approach to unify recent Noether type theorems on the equivalence of symmetries with conservation laws for…

There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable…

Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there…

We have studied a faded problem, the Jacobian Conjecture ~: \noindent {\sf The Jacobian Conjecture $(JC_n)$}~: If $f_1, \cdots, f_n$ are elements in a polynomial ring $k[X_1, \cdots, X_n]$ over a field $k$ of characteristic $0$ such that…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…

An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular…

A complete classification of non-affine dynamical quantum $R$-matrices obeying the ${\mathcal G}l_n({\mathbb C})$-Gervais-Neveu-Felder equation is obtained without assuming either Hecke or weak Hecke conditions. More general dynamical…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…