Representation type of Jordan algebras

Autor(es)

Kashuba, Iryna ^[1] ; Ovsienko, Serge ^[2] ; Shestakov, Ivan ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05311970 Sao Paulo - Brazil

^[2] Kiev Tarns Shevchenko Univ, Fac Mech & Math, UA-00133 Kiev - Ukraine

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 226, n. 1, p. 385-418, JAN 15 2011.
• Citações Web of Science: 5

Resumo

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 04/02850-2 - Sergiy Ovsiyenko | University Kiev - Ucrânia
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 05/60337-2 - Álgebras de Lie e de Jordan, suas representações e generalizações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 04/05979-6 - As representacoes das algebras de jordan.
• Beneficiário: Iryna Kashuba
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado