Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The extended affine Lie algebra associated with a connected non-negative unit form

Jasso, Gustavo LU (2014) In Journal of Algebra 409. p.148-161
Abstract
Given a connected non-negative unit form we construct an extended affine Lie algebra by giving a Chevalley basis for it. We also obtain this algebra as a quotient of an algebra defined by means of generalized Serre relations by M. Barot, D. Kussin and H. Lenzing. This is done in an analogous way to the construction of the simply-laced affine Kac–Moody algebras. Thus, we obtain a family of extended affine Lie algebras of simply-laced Dynkin type and arbitrary nullity. Furthermore, there is a one-to-one correspondence between these Lie algebras and the equivalence classes of connected non-negative unit forms.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Algebra
volume
409
pages
14 pages
publisher
Elsevier
external identifiers
  • scopus:84898886078
ISSN
0021-8693
DOI
10.1016/j.jalgebra.2014.03.029
language
English
LU publication?
no
id
fb4ba2de-eb4d-4f4d-a650-40bf2c0c5bdc
date added to LUP
2022-03-09 15:20:47
date last changed
2022-12-20 14:46:18
@article{fb4ba2de-eb4d-4f4d-a650-40bf2c0c5bdc,
  abstract     = {{Given a connected non-negative unit form we construct an extended affine Lie algebra by giving a Chevalley basis for it. We also obtain this algebra as a quotient of an algebra defined by means of generalized Serre relations by M. Barot, D. Kussin and H. Lenzing. This is done in an analogous way to the construction of the simply-laced affine Kac–Moody algebras. Thus, we obtain a family of extended affine Lie algebras of simply-laced Dynkin type and arbitrary nullity. Furthermore, there is a one-to-one correspondence between these Lie algebras and the equivalence classes of connected non-negative unit forms.}},
  author       = {{Jasso, Gustavo}},
  issn         = {{0021-8693}},
  language     = {{eng}},
  pages        = {{148--161}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Algebra}},
  title        = {{The extended affine Lie algebra associated with a connected non-negative unit form}},
  url          = {{http://dx.doi.org/10.1016/j.jalgebra.2014.03.029}},
  doi          = {{10.1016/j.jalgebra.2014.03.029}},
  volume       = {{409}},
  year         = {{2014}},
}