Related papers: Complete reducibility and isogenies over an arbitr…

We study the homogeneous involutions on the full square matrices over an algebraically closed field endowed with a division grading with commutative support. We obtain the classification of the isomorphism and equivalence classes for the…

Topological properties of the gauge field in a two-dimensional Higgs model are investigated. Results of exploratory numerical simulations are presented.

Space-times admitting a shear-free, irrotational, geodesic null congruence are studied. Attention is focused on those space-times in which the gravitational field is a combination of a perfect fluid and null radiation.

We present a clear and practical way to characterize the parabolicity of a complete immersed surface that is invariant with respect to a Killing vector field of the ambient space.

We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has…

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

Let $A$ be a finite-dimensional associative $k$-algebra with identity. The primary aim of this paper is to study the rationality properties of the group of all $k$-algebra automorphisms of $A$, as an affine algebraic group over an arbitrary…

Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p>0$. Let $E/K$ be an elliptic curve with a $K$-rational isogeny of prime degree $\ell$. In this article, we study the…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove that if $\mathbb{P}$ is the (uniform) Auslander condition, or…

The present paper is devoted to study some completeness properties of transitive binary relational set, i.e., a set together with a transitive binary relation (so called t-set).

We summarize the fall-off of electromagnetic and gravitational fields in n>5 dimensional Ricci-flat spacetimes along an asympotically expanding non-singular geodesic null congruence.

Let $G$ be a connected reductive linear algebraic group over a field $k$. Using ideas from geometric invariant theory, we study the notion of $G$-complete reducibility over $k$ for a Lie subalgebra $\mathfrak h$ of the Lie algebra…

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

The behaviour of Jacobi fields along a time-like geodesic running into an isotropic singularity is studied. It is shown that the Jacobi fields are crushed to zero length at a rate which is the same in every direction orthogonal to the…

We present a complete suite of algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic different from 2. This is a new version with numerous changes and improvements.

We consider the i.i.d. Bernoulli field $\mu_p$ with occupation density $p \in (0,1)$ on a possibly non-regular countably infinite tree with bounded degrees. For large $p$, we show that the quasilocal Gibbs property, i.e. compatibility with…

A simple algorithm is proposed for constructing generators of gauge symmetry as well as reducibility relations for arbitrary systems of field equations in two dimensions.

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that the elementary subgroup E(R) of group of points G(R) is correctly defined. Then E(R) is perfect, except for the well-known cases of a split reductive…

Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…