Invariants of Lie Algebras Extended Over Commutative Algebras Without Unit
- 10.1142/S1402925110000817How to use a DOI?
- Current Lie algebra; Kac–Moody algebras; second cohomology; invariant bilinear form; derivation
We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms, and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac–Moody algebras.
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Pasha Zusmanovich PY - 2021 DA - 2021/01/07 TI - Invariants of Lie Algebras Extended Over Commutative Algebras Without Unit JO - Journal of Nonlinear Mathematical Physics SP - 87 EP - 102 VL - 17 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000817 DO - 10.1142/S1402925110000817 ID - Zusmanovich2021 ER -