# On a nilpotent Lie superalgebra which generalizes Qn.

José María Ancochea Bermúdez; Otto Rutwig Campoamor

Revista Matemática Complutense (2002)

- Volume: 15, Issue: 1, page 131-146
- ISSN: 1139-1138

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topAncochea Bermúdez, José María, and Campoamor, Otto Rutwig. "On a nilpotent Lie superalgebra which generalizes Qn.." Revista Matemática Complutense 15.1 (2002): 131-146. <http://eudml.org/doc/44417>.

@article{AncocheaBermúdez2002,

abstract = {In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain central extensions of Qn which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras.},

author = {Ancochea Bermúdez, José María, Campoamor, Otto Rutwig},

journal = {Revista Matemática Complutense},

keywords = {Algebra de Lie; Algebra nilpotente; filiform Lie superalgebra},

language = {eng},

number = {1},

pages = {131-146},

title = {On a nilpotent Lie superalgebra which generalizes Qn.},

url = {http://eudml.org/doc/44417},

volume = {15},

year = {2002},

}

TY - JOUR

AU - Ancochea Bermúdez, José María

AU - Campoamor, Otto Rutwig

TI - On a nilpotent Lie superalgebra which generalizes Qn.

JO - Revista Matemática Complutense

PY - 2002

VL - 15

IS - 1

SP - 131

EP - 146

AB - In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain central extensions of Qn which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras.

LA - eng

KW - Algebra de Lie; Algebra nilpotente; filiform Lie superalgebra

UR - http://eudml.org/doc/44417

ER -

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