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.
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. It presents applications to population genetics theory, and physics.
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 dexistence dune 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.
R. Costa, Henrique Guzzo Jr., A. Grichkov, L.A. Peresi,
