Let K be a field and let A be a finitely generated prime K-algebra. We generalize a result of Smith and Zhang, showing that if A is not PI and does not have a locally nilpotent ideal, then the extended centre of A has transcendence degree at most GKdim(A) − 2 over K. As a consequence, we are able to show that if A is a prime K-algebra of quadratic growth, then either the extended centre is a fi...

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...

Let M be a Galois cover of a nilpotent coadjoint orbit of a complex semisimple Lie group. We define the notion of a perfect Dixmier algebra for M and show how this produces a graded (non-local) equivariant star product on M with several very nice properties. This is part of a larger program we have been developing for working out the orbit method for nilpotent orbits.

In this note we shall investigate a topological version of the problem of Kurosh: “Is any algebraic algebra locally finite?” Kaplansky’s theorem concerning the local nilpotence of nil PI-algebras is well-known. We will prove a generalization of Kaplansky’s theorem to the class of locally compact rings. We use in the proof a theorem of A. I. Shirshov [8] concerning the height of a finitely gener...

Our work is concerned with the problem on limit cycle bifurcation for a class of Z3-equivariant Lyapunov system of five degrees with three third-order nilpotent critical points which lie in a Z3-equivariant vector field. With the help of computer algebra system-MATHEMATICA, the first 5 quasiLyapunov constants are deduced. The fact of existing 12 small amplitude limit cycles created from the thr...

For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].

We study the maximal abelian ad-nilpotent (mad) subalgebras of the domains D Morita equivalent to the first Weyl algebra. We give a complete description both of the individual mad subalgebras and of the space of all such. A surprising consequence is that this last space is independent of D . Our results generalize some classic theorems of Dixmier about the Weyl algebra.

1 Divided Power Algebra—October 31, 2016 1 1.1 Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Extension of Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compatible Divided Power structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Divided Power Algebra Associated to a Module . . . . . . . . . . . . . . . . . 5 1.5...

In this work we provide a new short proof of Carlitz’s identity for the Bernoulli numbers. Our approach is based on the ordinary generating function for the Bernoulli numbers and a Grassmann-Berezin integral representation of the Bernoulli numbers in the context of the Zeon algebra, which comprises an associative and commutative algebra with nilpotent generators.