Dreieckverbande : lineare und quadratische darstellungstheorie
Date
1987-05
Authors
Wild, Marcel Wolfgang
Journal Title
Journal ISSN
Volume Title
Publisher
University of Zurich
Abstract
ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school (Wille, Herrmann, Poguntke, et al), to large extent triggered by the linear representations of posets (Gabriel, Gelfand-Ponomarev, Nazarova, Roiter, Brenner, et al). Even though posets are more general than lattices, none of the two theories encompasses the other. In my thesis a natural type of finite lattice is identified, i.e. triangle lattices, and their linear representation theory is advanced. All of this was triggered by a more intricate setting of quadratic spaces (as opposed to mere vector spaces) and the question of how Witt’s Theorem on the congruence of finite-dimensional quadratic spaces lifts to spaces of uncountable dimensions. That issue is dealt with in the second half of the thesis.
Description
Prof. Marcel Wild completed his PhD with Zurick University and this is a copy of the original works
The original works can be found at http://www.hbz.uzh.ch/
The original works can be found at http://www.hbz.uzh.ch/
Keywords
Modular lattices, Triangle lattices, Linear representation theory, Uncountable quadratic spaces, Dissertations -- Mathematics, Theses -- Mathematics