Related papers: *-Graded Capelli Polynomials and their Asymptotic

In this note, we will show that the twisted convolution algebra $L^1_{\alpha,\omega}({\sf G},\mathfrak A)$ associated to a twisted action of a locally compact group ${\sf G}$ on a $C^*$-algebra $\mathfrak A$ has the following property:…

We examine diagonal combs, a recently identified class of infinite metric graphs whose properties depend on one parameter. These graphs exhibit a fascinating regime where they possess infinite volume while maintaining purely discrete…

Let d>2 and let p be a prime coprime to d. Let Z_pbar be the ring of integers of Q_pbar. Suppose f(x) is a degree-d polynomial over Qbar and Z_pbar. Let P be a prime ideal over p in the ring of integers of Q(f), where Q(f) is the number…

Let $R$ be a Noetherian $\mathbb{N}$-graded ring. Let $L$, $M$ and $N$ be finitely generated graded $R$-modules with $N \subseteq M$. For a homogeneous ideal $I$, and for each fixed $k \in \mathbb{N}$, we show the asymptotic linearity of…

Let $\g$ be a reductive Lie algebra and $V$ a $\g$-semisimple module. In this article, we study the category $\G$ of graded finite-dimensional representations of $\g \ltimes V$. We produce a large class of truncated subcategories, which are…

A characterization of the finite-dimensional Leibniz algebras with an abelian subalgebra of codimension two over a field $\mathbb{F}$ of characteristic $p\neq2$ is given. In short, a finite-dimensional Leibniz algebra of dimension $n$ with…

If $\Delta$ and $\Gamma$ are two derivations of a commutative algebra $A$ such that $\Delta\Gamma-\Gamma\Delta=\Delta$ is locally nilpotent, one can endow $A$ with a new product $\ast$ whose filtered semiclassical limit is the Poisson…

Let P a locally finite partially ordered set, F a field, G a group, and I(P,F) the incidence algebra of P over F. We describe all the inequivalent elementary G-gradings on this algebra. If P is bounded, F is a infinite field of…

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that $\kappa,\lambda$ are infinite cardinals such that $\kappa^{+++} \leq \lambda$, $\kappa^{<\kappa}=\kappa$ and $2^{\kappa}= \kappa^+$, and…

Let $A$ be an associative algebra over a field $F$ of characteristic zero and let $L$ be a Lie algebra over $F$. If $L$ acts on $A$ by derivations, then such an action determines an action of its universal enveloping algebra $U(L)$ and in…

Let $K$ be a field and let $R = K[X_1, \ldots, X_m]$ with $m \geq 2$. Give $R$ the standard grading. Let $I$ be a homogeneous ideal of height $g$. Assume $1 \leq g \leq m -1$. Suppose $H^i_I(R) \neq 0$ for some $i \geq 0$. We show (1)…

We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces of genus g: m-hypermaps and m-constellations. For m=2, they correspond respectively to maps with even face degrees and bipartite maps. We obtain…

We give sufficient conditions, in terms of the existence of unbounded derivations satisfying certain properties, which ensure that a II$_1$ factor $M$ is prime or has at most one Cartan subalgebra. For instance, we prove that if there…

A locally compact group $G$ is a cocompact envelope of a group $\Gamma$ if $G$ contains a copy of $\Gamma$ as a discrete and cocompact subgroup. We study the problem that takes two finitely generated groups $\Gamma,\Lambda$ having a common…

We study 2-Calabi-Yau tilted algebras which are non-commutative Iwanaga-Gorenstein algebras of Gorenstein dimension 1. In particular, we are interested in their syzygy categories or equivalently the stable categories of Cohen-Macauley…

In this paper, we establish the asymptotic expressions for the gradient of a solution to the Lam\'{e} systems with partially infinity coefficients as two rigid $C^{1,\gamma}$-inclusions are very close but not touching. The novelty of these…

Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a…

Given a sequence $\{Z_d\}_{d\in \mathbb{N}}$ of smooth and compact hypersurfaces in $\mathbb{R}^{n-1}$, we prove that (up to extracting subsequences) there exists a regular definable hypersurface $\Gamma\subset \mathbb{R}\mathrm{P}^n$ such…

Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…

Aimed at geometric applications, we prove the homology cobordism invariance of the $L^2$-betti numbers and $L^2$-signature defects associated to the class of amenable groups lying in Strebel's class $D(R)$, which includes some interesting…