1. Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms
- Author
-
Junna Ni and Zhiqi Chen
- Subjects
Pure mathematics ,Integrable system ,Degenerate energy levels ,Statistical and Nonlinear Physics ,Bilinear form ,Mathematics::Algebraic Topology ,Algebra ,symbols.namesake ,Nilpotent ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Quadratic equation ,Mathematics::K-Theory and Homology ,symbols ,Novikov self-consistency principle ,Hamiltonian (quantum mechanics) ,Mathematical Physics ,Associative property ,Mathematics - 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.
- Published
- 2021