JORDAN BIMODULES OVER THE SUPERALGEBRAS P(n) AND Q(n)

Author(s)

Martinez, Consuelo ^[1] ; Shestakov, Ivan ^[2] ; Zelmanov, Efim ^{[3, 4]}

Affiliation

^[1] Univ Oviedo, Dept Matemat, Oviedo 33007 - Spain

^[2] Univ Sao Paulo, Inst Matemat & Estadist, BR-05315970 Sao Paulo - Brazil

^[3] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 - USA

^[4] Korea Inst Adv Study, Seoul 130012 - South Korea

• Document type: Journal article
• Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 362, n. 4, p. 2037-2051, APR 2010.
• Web of Science Citations: 3

Abstract

We extend the Jacobson's Coordinatization theorem to Jordan superalgebras. Using it we classify Jordan bimodules over superalgebras of types Q(n) and JP(n), n >= 3. Then we use the Tits-Kantor-Koecher construction and representation theory of Lie superalgebras to treat the remaining case Q(2). (AU)

• FAPESP's process: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants