Publication:
Contractions of Low-Dimensional Nilpotent Jordan Algebras

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2011
Authors
Fresán, Javier
Margalef Bentabol, Juan
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
In this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among their isomorphism classes. In particular, we prove that 2 and 3 are irreducible and that 4 is the union of the Zariski closures of the orbits of two rigid Jordan algebras
Description
UCM subjects
Unesco subjects
Keywords
Citation
Ancochea Bermúdez, J. M., Campoamor-Stursberg, R., García Vergnolle, L., Sánchez Hernández, J. (2008). Contractions d’algèbres de Jordan en dimension 2. J. Algebra 319:2395–2409. Ancochea Bermúdez, J. M., Goze, M. (1986). Sur la classification des algèbres de Lie nilpotentes de dimension 7. C. R. Acad. Sc.Paris 302:611–613. Gerstenhaber, M. (1964). On the deformation of rings and algebras. Ann. of Math. 79:59–103. Jacobson, N. (1968). Structure and Representation of Jordan Algebras. Vol. XXXIX. Providence, RI: AMS Colloquium Publications. Kashuba, I., Shestakov, I. (2007). Jordan algebras of dimension three: Geometric classification and representation type. Actas del XVI Coloquio Latinoamericano de Álgebra (Colonia del Sacramento, Uruguay). Bibl. Rev. Iber. Mat. 1:295–315. Kashuba, I. (2006). Variety of Jordan algebras in smal dimensions. Alg. Discrete Math. 3:62–76. Mazzola, G. (1978). Les composantes irréductibles du schéma des algébres de dimension 5. C. R. Acad. Sc. Paris Sér. A-B 286(8):A389–A390. Makhlouf, A. (1993). The irreducible components of the nilpotent associative algebras. Rev. Mat. Compl. 6:27–40. McCrimmon, K. (2004). A Taste of Jordan Algebras. New York: Springer-Verlag. Nijenhuis, A., Richardson, R. W. (1964). Cohomology and deformation of algebraic structures. Bull. Amer. Math. Society 70:406–411. Jordan, P., Neumann, J. V., Wigner, E. (1934). On an algebraic generalization of the quantum mechanics formalism. Ann. of Math. 35:29–64. Zel’manov, E. (1983). On prime Jordan algebras. II. Siberian Math. J. 24:73–85.
Collections