Representations of exceptional simple alternative superalgebras of characteristic 3
Authors:
M. C. López-Díaz and Ivan P. Shestakov
Journal:
Trans. Amer. Math. Soc. 354 (2002), 2745-2758
MSC (2000):
Primary 17D05, 17A70, 17C70
DOI:
https://doi.org/10.1090/S0002-9947-02-02993-8
Published electronically:
March 7, 2002
MathSciNet review:
1895201
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study representations of simple alternative superalgebras $B(1,2)$ and $B(2,4)$. The irreducible bimodules and bimodules with superinvolution over these superalgebras are classified, and some analogues of the Kronecker factorization theorem are proved for alternative superalgebras that contain $B(1,2)$ and $B(4,2)$.
- J. Bernad, S. González, C. Martínez, and A. V. Iltyakov, Polynomial identities of Bernstein algebras of small dimension, J. Algebra 207 (1998), no. 2, 664–681. MR 1644227, DOI https://doi.org/10.1006/jabr.1998.7475
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
- N.Jacobson, A Kronecker factorization theorem for Cayley algebras and the exceptional simple Jordan algebras, Amer. J. Math., 76 (1954), 447-452.
- Richard S. Pierce, Associative algebras, Graduate Texts in Mathematics, vol. 88, Springer-Verlag, New York-Berlin, 1982. Studies in the History of Modern Science, 9. MR 674652
- I. P. Shestakov, Prime alternative superalgebras of arbitrary characteristic, Algebra i Logika 36 (1997), no. 6, 675–716, 722 (Russian, with Russian summary); English transl., Algebra and Logic 36 (1997), no. 6, 389–412. MR 1657313, DOI https://doi.org/10.1007/BF02671556
- E. I. Zel′manov and I. P. Shestakov, Prime alternative superalgebras and the nilpotency of the radical of a free alternative algebra, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 4, 676–693 (Russian); English transl., Math. USSR-Izv. 37 (1991), no. 1, 19–36. MR 1073082
- K. A. Zhevlakov, A. M. Slin′ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, vol. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. Translated from the Russian by Harry F. Smith. MR 668355
Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 17D05, 17A70, 17C70
Retrieve articles in all journals with MSC (2000): 17D05, 17A70, 17C70
Additional Information
M. C. López-Díaz
Affiliation:
Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo, s/n, 33007, Oviedo, Spain
Email:
cld@pinon.ccu.uniovi.es
Ivan P. Shestakov
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 - CEP 05315-970, São Paulo, Brasil;
Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
MR Author ID:
289548
Email:
shestak@ime.usp.br
Keywords:
Alternative superalgebra and superbimodule,
superinvolution,
factorization theorem
Received by editor(s):
April 17, 2001
Published electronically:
March 7, 2002
Additional Notes:
The first author was supported by FAPESP 2000/03404-5 and FICYT PB-PGI 99-04
The second author was supported by CNPq grant 300528/99-0
Article copyright:
© Copyright 2002
American Mathematical Society
