On Lie algebras of classical type

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.

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

Classical Lie Algebras

Classical Lie algebras

1 Classical Lie algebras A Lie algebra is a vector space g with a bilinear map [, ] : g× g → g such that (a) [x, y] = −[y, x], for x, y ∈ g, and (b) (Jacobi identity) [x, [y, z]] + [z, [x, y]] + [y, [z, x]] = 0, for all x, y, z ∈ g. A bilinear form 〈, 〉 : g× g → C is ad-invariant if, for all x, y, z ∈ g, 〈adx(y), z〉 = −〈y, adx(z)〉, where adx(y) = [x, y], (1.1) for x, y,∈ g. The Killing form is ...

Fine Gradings on Simple Classical Lie Algebras

The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them.