TY - JOUR
T1 - Generators and relations for (generalised) Cartan type superalgebras
AU - Carbone, Lisa
AU - Cederwall, Martin
AU - Palmkvist, Jakob
N1 - Publisher Copyright:
© 2019 Published under licence by IOP Publishing Ltd.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/4/24
Y1 - 2019/4/24
N2 - In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n-1,0) = s (1|n) can be constructed by adding a "gray" node to the Dynkin diagram of An-1 = s (n), corresponding to an odd null root. The Cartan superalgebras constitute a difierent class, where the simplest example is Wpnq, the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of Wpnq, from the same Dynkin diagram as A(n-1,0), but with additional generators and relations.
AB - In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n-1,0) = s (1|n) can be constructed by adding a "gray" node to the Dynkin diagram of An-1 = s (n), corresponding to an odd null root. The Cartan superalgebras constitute a difierent class, where the simplest example is Wpnq, the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of Wpnq, from the same Dynkin diagram as A(n-1,0), but with additional generators and relations.
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U2 - 10.1088/1742-6596/1194/1/012020
DO - 10.1088/1742-6596/1194/1/012020
M3 - Conference article
AN - SCOPUS:85065595294
VL - 1194
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012020
T2 - 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018
Y2 - 9 July 2018 through 13 July 2018
ER -