Related papers: The deficiencies of Kaehler groups

We formulate Lehmer's Problem about the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant,…

We observe that upper densities and spherical Federer densities may differ on all two dimensional surfaces of the sub-Riemannian Heisenberg group. This provides an entire class of intrinsic rectifiable sets having upper density strictly…

The notion of essential submodules and essential extensions of modules are extended to groups (typically nonabelian), and several necessary and sufficient conditions for a group to possess a proper essential subgroup are investigated.…

Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $\l$-adic Lie extension ($\l\neq p$) unramified outside a finite set of primes $S$ and such that $\Gal(K/F)$ has no elements of order…

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the…

A group $G$ is said to have restricted centralizers if for each $g \in G$ the centralizer $C_G(g)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. We take…

We classify, up to isomorphism, gradings by abelian groups on nilpotent filiform Lie algebras of nonzero rank. In case of rank 0, we describe conditions to obtain non trivial $\Z_k$-gradings.

We describe certain almost-simple algebraic supergroups over an algebraically closed field of odd or zero characteristic. In addition to supergroups with simple Lie superalgebras from Kac's theorem, we construct new supergroups whose Lie…

This paper stems from the observation (arising from work of T. Delzant) that "most" K\"ahler groups virtually algebraically fiber, i.e. admit a finite index subgroup that maps onto $\Bbb{Z}$ with finitely generated kernel. For the remaining…

For a finite group $G$, we consider the zeta function $\zeta_G(s) = \sum_{H} \abs{H}^{-s}$, where $H$ runs over the subgroups of $G$. First we give simple examples of abelian $p$-group $G$ and non-abelian $p$-group $G'$ of order $p^m, \; m…

We address two fundamental and well-known problems of Gromov and Lyndon: \demo{Problem A} (Gromov, see [5]). Consider a category $M_n$ of closed manifolds of dimension $n$ with nonzero-degree ways as morphisms. Study a partial order $M \ge…

In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function $f$, they produce a finitely presented residually finite…

In this paper we describe all gradings by abelian groups without elements of order p, where p > 2 is the characteristic of the base field, on the simple graded Cartan type Lie algebras.

If K/F is a finite abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence that has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which we use to…

We prove a non-archimedean analogue of J{\o}rgensen's inequality, and use it to deduce several algebraic convergence results. As an application we show that every dense subgroup of $\mathrm{SL}(\mathbb{Q}_p)$ contains two elements which…

Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…

There are many known examples of scalar-flat K\"ahler ALE surfaces, all of which have group at infinity either cyclic or contained in ${\rm{SU}}(2)$. The main result in this paper shows that for any non-cyclic finite subgroup $\Gamma…

We study left-invariant locally conformally K\"ahler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is…