Hyperbolic Kac–Moody superalgebras

Abstract

We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank r ≥ 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root systems are determined. We also discuss a class of singular sub(super)algebras obtained by a folding procedure.MSC number: 17B65, 17B67

Ghost D-branes

“…One simple example is obtained from the D 5 Dynkin diagram (=7-brane configuration) by adding a fermionic node (=a ghost D7-brane) so that the Dynkin diagram becomes similar to E 6 (see e.g. [44]). It will also be interesting to see if we can obtain the affine Lie superalgebras from 7-brane configurations.…”

Vogan Diagrams of Untwisted Affine Kac–moody Superalgebras

“…The arrows will be added on the lines connecting the i-th and j-th dots when ζ ij > 1 and |a ij | = |a ji |, pointing from j to i if |a ij | > 1. One can get the different Dynkin diagrams with details in [6,5,8].…”

Embedding of simply laced hyperbolic Kac-Moody superalgebras

“…The constructs in this case so generated are hyperbolic Kac-Moody superalgebras. [4][5][6][7][8][9][10][11] Through the results of three papers, 1,3,12 it is now believed that the hyperbolic Kac-Moody superalgebras have also been completely classified. In all these papers it is also shown that similar to hyperbolic Kac-Moody algebras, the hyperbolic Kac-Moody superalgebras are also finite in number for rank >2 with maximum rank being 6.…”