Inner derivations of non-associative algebras

Inner Derivations of Non-associative Algebras

In this note we propose a definition of inner derivation for nonassociative algebras. This definition coincides with the usual one for Lie algebras, and for associative algebras with no absolute right (left) divisor of zero. I t is well known that all derivations of semi-simple associative or Lie algebras over a field of characteristic zero are inner. Recent correspondence with N. Jacobson has ...

Inner Derivations on Ultraprime Normed Algebras

We show that, for every ultraprime Banach algebra A, there exists a positive number γ satisfying γ‖a+Z(A)‖ ≤ ‖Da‖ for all a in A, where Z(A) denotes the centre of A and Da denotes the inner derivation on A induced by a. Moreover, the number γ depends only on the “constant of ultraprimeness” of A.

Deformations of Associative Algebras with Inner Products

We develop the deformation theory of A∞ algebras together with∞-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A∞ algebras, associative algebras with inner products, and A∞ algebras with inner products.

Non Associative Linear 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.