Abstract
Considering prime Leavitt path algebras
L
K
(
E
)
{L_{K}(E)}
, with E being an arbitrary graph with at least two vertices, and K being any field, we construct a class of maximal commutative subalgebras of
L
K
(
E
)
{L_{K}(E)}
such that, for every algebra A from this class, A has zero intersection with the commutative core
ℳ
K
(
E
)
{\mathcal{M}_{K}(E)}
of
L
K
(
E
)
{L_{K}(E)}
defined and studied in
[C. Gil Canto and A. Nasr-Isfahani,
The commutative core of a Leavitt path algebra,
J. Algebra 511 2018, 227–248].
We also give a new proof of the maximality, as a commutative subalgebra, of the commutative core
ℳ
R
(
E
)
{\mathcal{M}_{R}(E)}
of an arbitrary Leavitt path algebra
L
R
(
E
)
{L_{R}(E)}
, where E is an arbitrary graph and R is a commutative unital ring.
Biserial algebras via subalgebras and the path algebra of D4
