2,601 research outputs found
Hopf Algebras in General and in Combinatorial Physics: a practical introduction
This tutorial is intended to give an accessible introduction to Hopf
algebras. The mathematical context is that of representation theory, and we
also illustrate the structures with examples taken from combinatorics and
quantum physics, showing that in this latter case the axioms of Hopf algebra
arise naturally. The text contains many exercises, some taken from physics,
aimed at expanding and exemplifying the concepts introduced
Moduli of abelian surfaces, symmetric theta structures and theta characteristics
We study the birational geometry of some moduli spaces of abelian varieties
with extra structure: in particular, with a symmetric theta structure and an
odd theta characteristic. For a -polarized abelian surface, we show
how the parities of the influence the relation between canonical level
structures and symmetric theta structures. For certain values of and
, a theta characteristic is needed in order to define Theta-null maps. We
use these Theta-null maps and preceding work of other authors on the
representations of the Heisenberg group to study the birational geometry and
the Kodaira dimension of these moduli spaces.Comment: Final version. To appear in Commentarii Mathematici Helvetici (CMH
Solitons and admissible families of rational curves in twistor spaces
It is well known that twistor constructions can be used to analyse and to
obtain solutions to a wide class of integrable systems. In this article we
express the standard twistor constructions in terms of the concept of an
admissible family of rational curves in certain twistor spaces. Examples of of
such families can be obtained as subfamilies of a simple family of rational
curves using standard operations of algebraic geometry. By examination of
several examples, we give evidence that this construction is the basis of the
construction of many of the most important solitonic and algebraic solutions to
various integrable differential equations of mathematical physics. This is
presented as evidence for a principal that, in some sense, all soliton-like
solutions should be constructable in this way.Comment: 15 pages, Abstract and introduction rewritten to clarify the
objectives of the paper. This is the final version which will appear in
Nonlinearit
Questions about linear spaces
AbstractWe present three themes of interest for future research that require the cooperation of fairly large teams: 1.linear spaces as building blocks;2.data for an Atlas of linear spaces;3.morphisms of linear spaces
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