Automorphisms of associative algebras and noncommutative geometry
Mathematical Physics
2008-11-26 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the -deformed plane and the quantum group GLpq(2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced.
Keywords
Cite
@article{arxiv.math-ph/0306058,
title = {Automorphisms of associative algebras and noncommutative geometry},
author = {Aristophanes Dimakis and Folkert Muller-Hoissen},
journal= {arXiv preprint arXiv:math-ph/0306058},
year = {2008}
}
Comments
28 pages, some references added, several amendments of minor importance, remark on modular group in section 8 omitted, to appear in J. Phys. A