![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
In this article, we compute explicitly the supermultiplicities of the roots for the following Borcherds superalgebras associated with the colored Borcherds–Cartan matrices: (i) three different types of extended-hyperbolic Borcherds superalgebras; (ii) Borcherds superalgebras which are extensions by one simple imaginary root of finite type A
3, affine type , and hyperbolic type HA
1; (iii) Borcherds superalgebras with finite number of imaginary simple roots which are not mutually orthogonal but no real simple root; and (iv) Borcherds superalgebras with one real simple root and two nonorthogonal imaginary simple roots. The Kang and Kim superdimension formula is used for all the cases.
Key Words:
ACKNOWLEDGMENTS
The first author, N. Sthanumoorthy is pleased to state that the research has been sponsored by the University Grants Commission (UGC), Government of India, under the Emeritus Fellowship awarded to him.
The authors are also thankful to the referee, whose comments have been useful in revising the article in the present form.
Notes
Communicated by K. C. Misra.