相关论文: Infinite Simple Bol Loops

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.

Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.

Let V be a finite set of points in the plane, not contained in a line. Assume |V| = n is an odd number, and |L \cap V| \leq 3 for every line L which is spanned by V. We prove that every simple line L_{a,b} in V creates a simple wedge (i.e.,…

Some associativity properties of a loop can be interpreted as certain closure configuration of the corresponding 3-net. It was known that the smallest non-associative loops with the so called left Bol property have order 8. In this paper,…

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

We compute numerically the homology of several graph complexes in low loop orders, extending previous results.

We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of skew braces, our result gives a complete list of finite non-abelian simple groups which occur…

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…

The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.

Let $H$ be a finite quasisimple classical group, i.e. $H$ is perfect and $S:=H/Z(H)$ is a finite simple classical group. We prove in this paper that, excluding the cases when the simple group $S$ has a very exceptional Schur multiplier such…

The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.

A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.

We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the…

In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.