Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring

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})...

Automorphisms of Verardi Groups: Small Upper Triangular Matrices over Rings

Verardi’s construction of special groups of prime exponent is generalized, and put into a context that helps to decide isomorphism problems and to determine the full group of automorphisms (or at least the corresponding orbit decomposition). The groups in question may be interpreted as groups of unitriangular matrices over suitable rings. Finiteness is not assumed.

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

The computation of abelian subalgebras in the Lie algebra of upper-triangular matrices

This paper deals with the computation of abelian subalgebras of the solvable Lie algebra hn, of n × n upper-triangular matrices. Firstly, we construct an algorithm to find abelian Lie subalgebras in a given Lie algebra hn. This algorithm allows us to compute an abelian subalgebra up to a certain dimension. Such a dimension is proved to be equal to the maximum for abelian subalgebras of hn.

Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings