Non-Associative Algebra and Its Applications

The Third International Conference on Non-associative Algebra and its Applications was held in Oviedo (Spain) from July 12th to July 17th, 1993. The two previous Conferences were held in Novosibirsk and Tashkent respectively. The OrganisingCommittee ofthe Conference was composed ofSantos Gonzalez Jimenez from Oviedo University and Alberto Elduque and Consuelo Martinez from Zaragoza University. The Scientific Committee was made up of the following members: G. Benkart, University of Wisconsin, USA C. Burgueiio, University of La Frontera, CHILE A. Galindo, University of Madrid , SPAIN S. Gonzalez, University of Oviedo, SPAIN P. Holgate, University of London, ENGLAND N. Jacobson, University of Yale, USA W. Kaup, University of Tiibingen . GER~IANY E. Kleinfeld, Univesity of Iowa. USA A. J. Kostrikin, University of Moscow, RUSSIA K. McCrimmon, University of Virginia, USA A. Micali, University of Montpellier, FRANCE R. Moody, University of Alberta, CANADA H. C. Myung, University of Nort. hern Iowa. USA S. Okubo, University of Rochester, USA M. Osborn, University of Wisconsin. USA A. Perez de Vargas, University of Madrid. SPAIN H. Petersson, Fern-University, GERI\1AW{ M. Racine, University of Otawa, CANADA A. Rodriguez, University of Granada, SPAIN I. Shestakov, University of Novosibirsk, RUSSIA A. Slinko, University of Moscow. RUSSIA E. Taft, University of Rutgers, USA E. Zelmanov, University of Wisconsin. USA Unfortunately, one ofthem,Professor Philip Holgate, died some months before the Conference took place.

Klappentext

This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. br/ All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. br/ The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics. br/

Inhalt
Malcev superalgebras.- The first Tits construction of Albert algebras over locally ringed spaces.- The identity (x2)2 = ?(x)x3 in baric algebras.- Cayley-Klein Lie algebras and their quantum universal enveloping algebras.- On constructions of nonsolvable Lie algebras whose ideals are in chain.- Lie algebras graded by root systems.- Bernstein representations.- On free differentials on associative algebras.- On primitive Jordan Banach algebras.- Zel'manov's theorem for nondegenerately ultraprime Jordan-Banach algebras.- Jordan H-triple systems.- Prime alternative triple systems.- M-ideals of Schreier type and the Dunford-Pettis property.- Spectra of elements of a nonassociative algebra.- Ranges of elements of a nonassociative algebra.- Coordinatization of Jordan algebras over locally ringed spaces.- Sur la décomposition de Peirce.- On transitive left-symmetric algebras.- Spectral study of some topological Jordan algebras.- Representations of reduced enveloping algebras.- A cohomological characterization of solvable modular Lie algebras.- An extension of the Zel'manov-Goldie theorem.- On the unitarization of highest weight representations for affine Kac-Moody algebras.- Cohn's theorem for superalgebras.- On Bernstein algebras of n-th order.- On Bernstein algebras.- Realization of Lie algebras with polynomial vector fields.- Les algèbres de Kac-Moody et l'homologie dièdrale.- Quadratic differential equations in graded algebras.- Projective double Lie algebras on a Lie algebra.- On derivation algebras of group algebras.- J-diviseurs topologiques de zéro dans une algèbre de Jordan n.c. normée.- On Freudenthal-Kantor triple systems and generalized structurable algebras.- Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains.-Quadratic differential equations on graded structures.- A generalization of Novikov rings.- Automorphismes et dérivations dans les algèbres de Barker.- Lattice isomorphisms of Jordan algebras over arbitrary fields.- Multibaric algebras.- The Bernstein Problem in mathematical genetics and Bernstein algebras.- Les algèbres de mutation.- Non associative graded algebras.- Tracial elements for nonassociative H-algebras.- On lattice isomorphism of Bernstein algebras.- Bernstein algebras whose lattice ideals is linear.- Local algebras.- Applications of fox differential calculus to free Lie superalgebras.- On the cohomology for the Witt algebra w(1,1).- 3-graded Lie algebras and Jordan pairs.- Super-triple systems, normal and classical Yang-Baxter equations.- A conjecture on locally Novikov algebras.- Coalgebra, cocomposition and cohomology.- Minimal polynomial identities of bark algebras.- On power associative composition algebras.- Enumeration and classification of Albert algebras: reduced models and the invariants mod 2.- Composition algebras over open dense subschemes of curves of genus zero.- Simple Jordan superalgebras.- Absolute valued algebras of degree two.- On a generalization of the Jordan inverse.- On geodesic loops of trans-symmetric space.- Quadratic systems, blow-up, and algebras.- Quantization of Poisson superalgebras and speciality of Jordan Poisson superalgebras.- Duplicated algebras of algebras.- aux algèbres de Bernstein périodiques.- Randon Jordan derivations.- Randon derivations on H*-algebras.- Algebras of rank three.- Inner product characterizations of classical Cayley-Dickson algebras.- Sur les ?-algèbras de Jordan non commutatives, de division, de dimension 8, possédant un automorphisme ou une dérivation non triviaux.