Skip to main content Accessibility help
×
Home

JORDAN BIMODULES OVER THE SUPERALGEBRA M1|1

  • CONSUELO MARTÍNEZ (a1) and IVAN SHESTAKOV (a2)

Abstract

Let F be a field of characteristic different of 2 and let M1|1(F)(+) denote the Jordan superalgebra of 2 × 2 matrices over the field F. The aim of this paper is to classify irreducible (unital and one-sided) Jordan bimodules over the Jordan superalgebra M1|1(F)(+).

Copyright

References

Hide All
1.Bahturin, Y., Goze, M. and Remm, E., Group gradings on lie algebras, with applications to geometry, I, in Developments and Retrospectives in Lie Theory: Algebraic Methods (Mason, G., Penkov, I. and Wolf, J. A., Editors) (Springer, Switzerland, 2014), 151.
2.Elduque, A. and Kochetov, M., Gradings on Simple Lie Algebras, Mathematical surveys and Monographs, vol. 189 (American Mathematical Society, Providence, RI, 2013).
3.Jacobson, N., Structure and Representation of Jordan Algebras, vol. XXXIX (American Mathematical Society Colloquium Publications, Providence, 1968).
4.Kac, V. G., Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra 5(13) (1977), 13751400.
5.Martínez, C., Shestakov, I. and Zelmanov, E., Jordan superalgebras defined by brackets, J. London Math. Soc. 64(2) (2001), 357368.
6.Martínez, C., Shestakov, I. and Zelmanov, E., Jordan bimodules over the superalgebras P(n) and Q(n), Trans. Am. Math. Soc. 362(4) (2010), 20372051.
7.Martínez, C. and Zelmanov, E., Simple finite-dimensional Jordan superalgebras of prime characteristic, J. Algebra 236(2) (2001), 374444
8.Martínez, C. and Zelmanov, E., Specializations of Jordan superalgebras, Canad. Math. Bull. 45(4) (2002), 653671.
9.Martínez, C. and Zelmanov, E., Unital Jordan bimodules over the simple Jordan superalgebra D(t), Trans. Am. Math. Soc. 358(8) (2006), 36373649.
10.Martínez, C. and Zelmanov, E., Jordan superalgebras and their representations, Contemp. Math. 483 (2009), 179194.
11.Martínez, C. and Zelmanov, E., Representation theory of Jordan Superalgebras I, Trans. Am. Math. Soc. 362(2) (2010), 815846.
12.Martínez, C. and Zelmanov, E., Irreducible representations of the exceptional Cheng-Kac superalgebra, Trans. Am. Math. Soc. 366(11) (2014), 58535876.
13.Racine, M. and Zelmanov, E., Simple Jordan superalgebras with semisimple even part, J. Algebra 270(2) (2003), 374444.
14.Shtern, A. S., Representations of finite-dimensional Jordan superalgebras of Poisson brackets, Comm. Algebra 23(5) (1995), 18151823.
15.Solarte, O. F. and Shestakov, I., Irreducible specializations of the simple Jordan superalgebra of Grassmann Poisson bracket, J. Algebra 455 (2016), 291313.
16.Trushina, M., Modular representations of the Jordan superalgebras D(t), J. Algebra 320(4) (2008), 13271343.

MSC classification

JORDAN BIMODULES OVER THE SUPERALGEBRA M1|1

  • CONSUELO MARTÍNEZ (a1) and IVAN SHESTAKOV (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.