This book contains the proceedings of the 5th international conference on nonassociative algebra and its applications held in the summer of 2003 in Mexico. The book is dedicated to the memory of one of its editors, Lev Sabinin, who passed away after the meeting when the proceedings were being edited. The theory of nonassociative algebras has expanded a lot over the past two decades and has now reached a stage of maturity and great depth in fields as diverse as Lie algebras, nonassociative rings and algebras, quasigroups and loops, and applications of all these to physics and other natural sciences. The present volume contains essays and paper in all these areas (33 in total) giving thus a picture of the current state of work in nonassociative algebras.
The book includes papers on the theory of free Lie algebras (L. Bokut and E.S. Chibrikov), an overview of Kikkawa spaces in the context of the theory of smooth loops and smooth modules (R. Carrillo-Catalán), a survey on approximation of locally compact groups by finite groups, semigroups and quasigroups (L.Y. Glebsky, E.I. Gordon and C.J. Rubio), an up-to-date overview of nonassociative geometry, discrete models of spacetime, their continuous limits and the associated causal structure (A.I. Nesterov), a reformulation of the Sabinin principle in operadic terms (E. Paal) and a survey (Sabinin and L. V. Sbitneva) on recent research in algebras (quasigroups and loops, the geometry of Lie groups, Lie algebras and homogeneous spaces with applications) and mathematical physics (the loopuscular approach to discrete spacetime).