On the solvability of graded Novikov algebras

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

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...

On Associativity of Graded Algebras

Necessary and sufficient conditions are given to guarantee associativity of algebras and co-algebras. As main application, it is discussed the associativity of the tensor algebra T (V ) of a free module V over any commutative ring R. 1. Review of basic definitions Recall that a vector space A, or more generally a (free) module over a commutative ring R is an R-algebra if a multiplication map mA...

Fermionic Novikov Algebras Admitting Invariant Non-degenerate Symmetric Bilinear Forms Are Novikov Algebras

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 i...

Involutions on graded matrix algebras