Zachary Mesyan

Simple Lie algebras arising from Leavitt path algebras

For a field K and directed graph E, we analyze those elements of the Leavitt path algebra LK(E) which lie in the commutator subspace [LK(E),LK(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to determine which Lie algebras of the form [LK(E),LK(E)] are simple, when E is row-finite (i.e., has finite out-degree) and LK(E) is simple.

Generating Self-Map Monoids of Infinite Sets

Let

Polynomials of small degree evaluated on matrices

Omega

The structure of a graph inverse semigroup

be a countably infinite set,

On Minimal Extensions of Rings

S = {rm Sym}(Omega)

Infinite-dimensional diagonalization and semisimplicity

the group of permutations of

TRACES ON SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS

Omega

Commutator Leavitt Path Algebras

, and

THE IDEALS OF AN IDEAL EXTENSION

E = {rm Self}(Omega)

Infinite-dimensional triangularization

the monoid of self-maps of