相关论文: On Vlasenko's formal group laws

The Ehresmann-Schein-Nambooripad theorem gives a structure theorem for inverse monoids: they are inductive groupoids. A particularly nice case due to Jarek is that commutative inverse monoids become semilattices of abelian groups. It has…

We describe the automorphism groups of finite $p$-groups arising naturally via Hessian determinantal representations of elliptic curves defined over number fields. Moreover, we derive explicit formulas for the orders of these automorphism…

Let $k$ be a finitely generated field, let $X$ be an algebraic variety and $G$ a linear algebraic group, both defined over $k$. Suppose $G$ acts on $X$ and every element of a Zariski-dense semigroup $\Gamma \subset G(k)$ has a rational…

The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it is a finite dimensional Hopf algebra, to the `many-object'…

The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While…

We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a semi-norm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f.…

Following ideas of Arnold and Seigal-Yakovenko, we prove that the space of matrix coefficients of a formal Lie group action belongs to a Noetherian ring. Using this result we extend the uniform intersection multiplicity estimates of these…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

As an extension of previous ungraded work, we define a graded $p$-polar ring to be an analog of a graded commutative ring where multiplication is only allowed on $p$-tuples (instead of pairs) of elements of equal degree. We show that the…

The well-known Formanek's module finiteness theorem states that every unital prime PI-algebra (i.e. a central order in a matrix algebra by Posner's theorem) embeds into a finitely generated module over its center. An analogue of this…

Let $G$ be a reductive algebraic group over a $p$-adic field or number field $K$, and let $V$ be a $K$-linear faithful representation of $G$. A lattice $\Lambda$ in the vector space $V$ defines a model $\hat{G}_{\Lambda}$ of $G$ over…

Let $W$ be a rank $n$ irreducible finite reflection group and let $p_1(x),\ldots,p_n(x)$, $x\in\mathbb{R}^n$, be a basis of algebraically independent $W$-invariant real homogeneous polynomials. The orbit map $\overline…

The Donald--Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and for the classical Weyl groups (whose rational group…

Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of $\mathbb Z^n$-graded modules. We consider them in the setting of local graded rings $R$, with grading over an abelian group, and give a…

We classify group schemes in terms of their Cartier modules. We also prove the equivalence of different definitions of the tangent space and the dimension for these group schemes; in particular, the minimal dimension of a formal group law…

We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the $\mathbb{F}_q$-isomorphism classes…

We utilize the structure of quasiautomorphic forms over a Hecke triangle group to define a mapping from a quasiautomorphic form to a vector-valued automorphic form (vvaf). This kind of vvaf we call a Hecke vector-form. First we supply a…

We develop an extension of the usual theory of formal group laws where the base ring is not required to be commutative and where the formal variables need neither be central nor have to commute with each other. We show that this is the…

Let $G$ be a finite group and let $p$ be a prime. In this paper, we study the structure of finite groups with a large number of $p$-regular conjugacy classes or, equivalently, a large number of irreducible $p$-modular representations. We…

Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic $p>0$ developed by Symonds and the author, we give a characterization…