NonasSociative Algebra and Its Applications  book cover
1st Edition

NonasSociative Algebra and Its Applications

ISBN 9780824704063
Published April 18, 2000 by CRC Press
488 Pages

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Book Description

A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.

Table of Contents

Preface -- Contributors -- New approach to octonions and Cayley algebras /Helena Albuquerque and Shahn Majid -- Identities of graded alternative algebras /Y. Bahturin and M. Zaicev -- Invariant connections on symmetric spaces /Pilar Benito, Cristina Draper, and Alberto Elduque -- £-ideals in Bernstein algebras /A. Catalan -- Octonions and affine connections on spheres /Alberto Elduque and Hyo Chul Myung -- Immediate applications of a new classification of finite dimensional simple Lie algebras /Mohammed El Houari -- An approach to integrable theories in any dimension: the role of non-semi simple Lie algebras /Luiz A. Ferreira -- Versal deformations of Lie algebras /Alice Fialowski -- Derivations in second order Bernstein algebras /M. A. Garcia-Muniz and C. Martinez -- Algebraic structure of the non-abelian Toda models /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Alternative rings of small order and the hunt for Moufang circle loops /Edgar G. Goodaire -- A note on linearization of some identities /H. Guzzo, Jr., and P. Vicente -- The commuting nucleus of right alternative rings /Irvin Roy Hentzel -- A construction of Jordan superalgebras from Jordan-Lie triple systems /Noriaki Kamiya and Susumu Okubo -- Rings with (x,y,z) = (x,z,y) /Erwin Kleinfeld and Margaret Kleinfeld -- On the semi simplicity of special Jordan superalgebras /Carlos Gomez-Ambrosi and Jesus Laliena -- Bernstein superalgebras of dimension four /S. Gonzalez, C. Lopez-Diaz, and C. Martinez -- Banach-Bemstein algebras and their applications /Yu. Lyubich -- Jordan superalgebras /C. Martinez -- Derivations of structurable / /*-algebras /J. Martinez Moreno -- Lie mappings of C* -algebras /Martin Mathieu -- Sur des anneaux commutatifs a puissances associatives de caracteristique premiere p> 0 /Joao Carlos da Motta Ferreira and Artibano Micali -- Principal ^-bundles /Alexander I. Nesterov -- Z x Z-graded Lie algebras containing a Heisenberg algebra /J. Marshall Osborn and Kaiming Zhao -- A„(l) Toda solitons: a relation between dressing transformations and vertex operators /H. Belich and R. Paunov -- Generalized quadratic rings /Luiz Antonio Peresi -- The derivation algebra of a division composition algebra /J. M. Perez-Izquierdo -- On the structure of the simple Moufang loop GLL (F2) /M. L. Merlini Giuliani and Cesar Polcino Milies -- Lie groups, differential geometry, and nonlinear integrable systems /A V. Razumov and M. V. Saveliev -- Smooth quasigroups and loops. Recent achievements and open problems /L. V. Sabinin -- On smooth left square distributive quasigroup /Liudmila Sabinina -- Algebraic structure of trans symmetric spaces /L. V. Sbitneva -- Bernstein algebras whose lattice of ideals is distributive /C. Martinez and J. Setd -- Specialty problem for Malcev algebras and Poisson Malcev algebras /Ivan P. Shestakov -- Applications of Lie ring methods to group theory /Pavel Shumyatsky -- Computable rings, groups and their isomorphisms /Bakhadyr Khoussainov and Arkadii Slinko -- Quantum F-algebras /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Conditions d’existence d’une loi de Hardy-Weinberg periodique dans des populations selectivement neutres /C. Mallol and R. Varro -- Finite semi fields three-dimensional over the left nuclei /G. P. Wene -- Supplementing radicals of nonassociative rings /Richard Wiegandt.

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