Smooth loops, fibre bundles and non-associative gauge theories
by
Alexander I. Nesterov
Universidad de Guadalajara, México

Oral Communication

Lie group theory has been extraordinarily successfull in the development of modern physics, in particular, in the description of the strong, weak, and electromagnetic interactions. However, available difficulties to unify all interactions prompt to look for a mathematical structure beyond groups. For instance, the quantum group approach is a construction of this type where the Lie group symmetry is replaced by a quantum group symmetry and the latter reduced to the standard one in the some limit. An other possibility is a non-associative generalization of the Lie group, such as quasigroups and smooth loops. In our talk we introduce the nonassociative generalization of principal fibre bundles and discuss new kind of gauge theories which involve ``higher non-associative gauge symmetries''

Date received: June 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-23.