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.
"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 E-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-semisimple Lie algebras Luiz A. Ferreira Versal deformations of Lie algebras Alice Fialowski Derivations in second order Bernstein algebras M. A. Garcia-Muñiz and C. Martínez Algebraic structure of the non-abelian Toda models J. F. Gomes, F. E. MendoncCa 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 semisimplicity of special Jordan superalgebras Carlos Gomez-Ambrosi and Jesus Laliena Bernstein superalgebras of dimension four S. González, C. López-Díaz, and C. Martínez Banach--Bernstein algebras and their applications Yu. Lyubich Jordan superalgebras C. Martínez Derivations of structurable H*-algebras J. Martínez Moreno Lie mappings of C*-algebras Martin Mathieu Sur des anneaux commutatifs à puissances associatives de caractéristique première p > 0 João Carlos da Motta Ferreira and Artibano Micali Principal Q-bundles Alexander I. Nesterov Z x Z-graded Lie algebras containing a Heisenberg algebra J. Marshall Osborn and Kaiming Zhao An(1) 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 César 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 transsymmetric spaces L. V. Sbitneva Bernstein algebras whose lattice of ideals is distributive C. Martínez and J. Setó Speciality 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 Khoussaino and Arkadii Slinko Quantum V-algebras J. F. Gomes, F. E. MendoncCa da Silveira, G. M. Sotkov, and A. H. Zimerman Conditions d'existence d'une loi de Hardy-Weinberg périodique dans des populations sélectivement neutres C. Mallol and R. Varro Finite semifields three-dimensional over the left nuclei G. P. Wene Supplementing radicals of nonassociative rings Richard Wiegandt "