Realization of simple Lie algebras via Hall algebras of tame hereditary algebras

On Ringel-hall Algebras of Tame Hereditary Algebras

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

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.

Realization of locally extended affine Lie algebras of type $A_1$

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Domestic Canonical Algebras and Simple Lie Algebras

For each simply-laced Dynkin graph ∆ we realize the simple complex Lie algebra of type ∆ as a quotient algebra of the complex degenerate composition Lie algebra L(A) 1 of a domestic canonical algebra A of type ∆ by some ideal I of L(A) 1 that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of L(A) 1 /I has a basis given by the coset o...