Fermionic Novikov Algebras Admitting Invariant Non-degenerate Symmetric Bilinear Forms Are Novikov Algebras
نویسندگان
چکیده
Gelfand and Dikii gave a bosonic formal variational calculus in [5, 6] and Xu gave a fermionic formal variational calculus in [13]. Combining the bosonic theory of Gelfand-Dikii and the fermionic theory, Xu gave in [14] a formal variational calculus of super-variables. Fermionic Novikov algebras are related to the Hamiltonian super-operator in terms of this theory. A fermionic Novikov algebra is a finite-dimensional vector space A over a field F with a bilinear product (x, y) 7→ xy satisfying
منابع مشابه
Novikov Structures on Solvable Lie Algebras
We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable. Conversely we present an example of a nilpotent 2-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matrices and via extensions. In the latter case we lift No...
متن کاملClassical R-matrices and Novikov Algebras
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.
متن کاملLoop Algebras and Bi-integrable Couplings∗
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the s...
متن کامل5 S ep 2 00 6 Non - degenerate bilinear forms in characteristic 2 , related contact forms , simple Lie algebras and superalgebras
Non-degenerate bilinear forms over fields of characteristic 2, in particular, nonsymmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are two series of distinct finite simple Chevalley groups preserving the non-degenerate symmetric bilinear forms on the space of even dimension, the description of...
متن کاملJa n 20 06 Non - degenerate bilinear forms in characteristic 2 , related contact forms , simple
Non-degenerate bilinear forms over fields of characteristic 2, in particular, nonsymmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are two series of distinct finite simple Chevalley groups preserving the non-degenerate symmetric bilinear forms on the space of even dimension, the description of...
متن کامل