Abstract
In this paper is defined the notion of Bernstein representation and it is proved that every irreducible module over a nuclear Bernstein algebra is one-dimensional.
The notion of universal representation of a Bernstein algebra is also introduced and some properties of this algebra are estudied by using properties of the given algebra.
Partially supported by D.G.A. P. CB-6/91.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I.R.HENTZEL and L.A.PERESI, “Semiprime Bernstein algebras”, Arch.math, 52 (1989) 534–593.
N.JACOBSON, “Structure and Representations of Jordan algebras”, American Mathematical Society Colloquim Publications 1968.
Yu.A.MEDVEDEV and E.I.ZEL’MANOV, “Solvable Jordan algebras”, Comm.Alg, 13 (6), 1389–1414 (1985).
E.I.ZEL’MANOV and V.G.SKOSYRSI II, “Special Jordan nilalgebras of bounded index”, Algebra i Logica, vol.22, n6, 626–635.
A.WÖRZ-BUSEKROS, “Algebras in Genetics”, Lecture Notes in Biomathematics 36, Berlin-Heidelberg-New York 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bernad, J., Iltyakov, A., Martinez, C. (1994). Bernstein Representations. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-0990-1_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4429-5
Online ISBN: 978-94-011-0990-1
eBook Packages: Springer Book Archive