150 research outputs found
Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
The present text surveys some relevant situations and results where basic
Module Theory interacts with computational aspects of operator algebras. We
tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be
published in Lecture Notes in Computer Scienc
The Differential Dimension Polynomial for Characterizable Differential Ideals
We generalize the differential dimension polynomial from prime differential
ideals to characterizable differential ideals. Its computation is algorithmic,
its degree and leading coefficient remain differential birational invariants,
and it decides equality of characterizable differential ideals contained in
each other
On the cohomology of Galois groups determined by Witt rings
Let F denote a field of characteristic different from two. In this paper we
describe the mod 2 cohomology of a Galois group which is determined by the Witt
ring WF
Semi-direct products of Lie algebras and their invariants
The goal of this paper is to extend the standard invariant-theoretic design,
well-developed in the reductive case, to the setting of representation of
certain non-reductive groups. This concerns the following notions and results:
the existence of generic stabilisers and generic isotropy groups for
finite-dimensional representations; structure of the fields and algebras of
invariants; quotient morphisms and structure of their fibres. One of the main
tools for obtaining non-reductive Lie algebras is the semi-direct product
construction. We observe that there are surprisingly many non-reductive Lie
algebras whose adjoint representation has a polynomial algebra of invariants.
We extend results of Takiff, Geoffriau, Rais-Tauvel, and Levasseur-Stafford
concerning Takiff Lie algebras to a wider class of semi-direct products. This
includes -contractions of simple Lie algebras and generalised Takiff
algebras.Comment: 49 pages, title changed, section 11 is shortened, numerous minor
corrections; accepted version, to appear in Publ. RIMS 43(2007
Towards a Model Theory for Transseries
The differential field of transseries extends the field of real Laurent
series, and occurs in various context: asymptotic expansions, analytic vector
fields, o-minimal structures, to name a few. We give an overview of the
algebraic and model-theoretic aspects of this differential field, and report on
our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p
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