Generators and relations for (generalised) Cartan type superalgebras
Paper in proceedings, 2019

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.

Author

Lisa Carbone

Rutgers University

Martin Cederwall

Chalmers, Physics, Theoretical Physics

Jakob Palmkvist

Chalmers, Physics, Theoretical Physics

Journal of Physics: Conference Series

17426588 (ISSN) 17426596 (eISSN)

Vol. 1194 1 012020

32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018
Prague, Czech Republic,

Beyond space and time

Swedish Research Council (VR), 2016-01-01 -- 2019-12-31.

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

Roots

Basic sciences

DOI

10.1088/1742-6596/1194/1/012020

More information

Latest update

11/8/2019