TY - JOUR
T1 - Divided power (co)homology. presentations of simple finite dimensional modular lie superalgebras with cartan matrix
AU - Bouarroudj, Sofiane
AU - Grozman, Pavel
AU - Lebedev, Alexei
AU - Leites, Dimitry
PY - 2010
Y1 - 2010
N2 - For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we explicitly give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras with indecomposable Cartan matrix in characteristic 2 (and - in the arXiv version of the paper - in other characteristics for completeness of the picture). In the modular and super cases, we define notions of Chevalley generators and Cartan matrix, and an auxiliary notion of the Dynkin diagram. The relations of simple Lie algebras of the A, D, E types are not only Serre ones. These non-Serre relations are same for Lie superalgebras with the same Cartan matrix and any distribution of parities of the generators. Presentations of simple orthogonal Lie algebras having no Cartan matrix (indigenous for characteristic 2) are also given.
AB - For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we explicitly give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras with indecomposable Cartan matrix in characteristic 2 (and - in the arXiv version of the paper - in other characteristics for completeness of the picture). In the modular and super cases, we define notions of Chevalley generators and Cartan matrix, and an auxiliary notion of the Dynkin diagram. The relations of simple Lie algebras of the A, D, E types are not only Serre ones. These non-Serre relations are same for Lie superalgebras with the same Cartan matrix and any distribution of parities of the generators. Presentations of simple orthogonal Lie algebras having no Cartan matrix (indigenous for characteristic 2) are also given.
KW - Defining relation
KW - Divided power cohomology
KW - Modular Lie superalgebra
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U2 - 10.4310/HHA.2010.v12.n1.a13
DO - 10.4310/HHA.2010.v12.n1.a13
M3 - Article
AN - SCOPUS:77954626103
SN - 1532-0073
VL - 12
SP - 237
EP - 278
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
IS - 1
ER -