Volume 17, Issue 2, June 2010, Pages 159 - 166
Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms
Authors
Junna Ni
Department of Mathematics, South China Normal University, 510631, P. R. China
Zhiqi Chen*
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China,chenzhiqi@nankai.edu.cn
*Corresponding author.
Corresponding Author
Zhiqi Chen
Received 18 July 2009, Accepted 4 December 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000684How to use a DOI?
- Keywords
- Novikov super-algebra; Novikov algebra; quadratic Novikov super-algebra; quadratic Novikov algebra; Lie-super algebra
- Abstract
Novikov super-algebras are related to quadratic conformal super-algebras which correspond to Hamiltonian pairs and play fundamental role in completely integrable systems. In this paper, we focus on quadratic Novikov super-algebras, which are Novikov super-algebras with associative non-degenerate super-symmetric bilinear forms. We show that quadratic Novikov super-algebras are associative and the associated Lie-super algebras of quadratic Novikov super-algebras are 2-step nilpotent. Moreover, we give some properties on quadratic Novikov super-algebras and classify the associated Lie-super algebras of quadratic Novikov super-algebras up to dimension 7.
- Copyright
- © 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 - Junna Ni AU - Zhiqi Chen PY - 2021 DA - 2021/01/07 TI - Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms JO - Journal of Nonlinear Mathematical Physics SP - 159 EP - 166 VL - 17 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000684 DO - 10.1142/S1402925110000684 ID - Ni2021 ER -