Centre of an algebra

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.

Non-additive Lie centralizer of infinite strictly upper triangular matrices

‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...

A New Integral Basis for the Centre of the Hecke Algebra of Type a Andrew Francis and Lenny Jones

We describe a recursive algorithm that produces an integral basis for the centre of the Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys–Murphy elements. We also discuss the existence of integral bases for the centre of the Hecke algebra that consist solely of monomial symmetric polynomials of Jucys–Murphy elements. Finally, for n = 3, we show...

Existence of an Algebra Norm on Certain Subalgebras of C(X)

On subalgebras of an evolution algebra of a "chicken" population

We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. For such algebras in terms of its structure constants we calculate right and plenary periods of generator elements. Some results on subalgebras of EACP and ideals on low-dimensional EACP are obtained.