Finitely sorting Lie algebras

Some non-finitely presented Lie Algebras

Let L be a free Lie algebra over a field k, I a non-trivial proper ideal of L, n > 1 an integer. The multiplicator H2(L/I , k) of L/I is not finitely generated, and so in particular, L/I is not finitely presented, even when L/I is finite dimensional.

Lie $^*$-double derivations on Lie $C^*$-algebras

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Finitely Presented Heyting Algebras

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

Lie Groups and Lie Algebras

Some properties of nilpotent Lie algebras

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.