In a previous work of the authors, a middle convolution operation on the category of Fuchsian differential systems was introduced. In this note we show that the middle convolution of Fuchsian systems preserves the property of global nilpotence. This leads to a globally nilpotent Fuchsian system of rank two which does not belong to the known classes of globally nilpotent rank two systems. Moreov...

A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is hyperfinite. In this paper we show that this question has a positive answer when the acting group is locally nilpotent. This extends previous results obtained by Gao–Jackson for abelian groups and by Jackson–Kechris–L...

The notable exclusions from the family of automatic groups are those nilpotent groups which are not virtually abelian, and the fundamental groups of compact 3-manifolds based on the Nil or Sol geometries. Of these, the 3-manifold groups have been shown by Bridson and Gilman to lie in a family of groups defined by conditions slightly more general than those of automatic groups, that is, to have ...

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

Let z = (z1, · · · , zn) and ∆ = ∑n i=1 ∂ 2 ∂z i the Laplace operator. The main goal of the paper is to show that the wellknown Jacobian conjecture without any additional conditions is equivalent to the following what we call vanishing conjecture: for any homogeneous polynomial P (z) of degree d = 4, if ∆P(z) = 0 for all m ≥ 1, then ∆P(z) = 0 when m >> 0, or equivalently, ∆P(z) = 0 when m > 3 2...

The purpose of this paper is to describe structural properties of automata whose transition semigroups have a zero, left zero, right zero or bi-zero, or are nilpotent extensions of rectangular bands, left zero bands or right zero bands, or are nilpotent. To describe the structure of these automata we use various well-known decomposition methods of automata theory – direct sum decompositions, su...

The local, covariant, continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry transformations are derived for a one (0+1)-dimensional free scalar relativistic particle in the framework of superfield formalism. The trajectory (i.e. the worldline) of the free particle, parametrized by a monotonically varying evolution parameter τ , is embedded in aD-dimensional flat Minkowsk...

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

We consider non-degenerate graph immersions into affine space An+1 whose cubic form is parallel with respect to the Levi-Civita connection of metric. There exists a correspondence between such and pairs (J,?), where J an n-dimensional real Jordan algebra ? trace on J. Every immersion can be extended complete symmetric covering maximal connected component zero in set quasi-regular elements It im...

In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truth-values as truth constants in the language and by adding corresponding book-keeping axioms for the truth-constants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong stan...