Maximal Commutative Subalgebras of Steinberg Algebras

2025/07/29 by Cichocka, Anna, Mesyan, Zachary, Ziembowski, Michal
#16S36 #16S88 #18B40 #22A22 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2507.21424

Abstract

We construct large classes of maximal commutative subalgebras in prime Steinberg algebras, generalizing a known result for Leavitt path algebras.

Citations

• Realizing ultragraph Leavitt path algebras as Steinberg algebras
• Étale groupoids and Steinberg algebras, a concise introduction
• The groupoid approach to Leavitt path algebras
• Prime 'etale groupoid algebras with applications to inverse semigroup\n and Leavitt path algebras
• The maximum dimension of a Lie nilpotent subalgebra of M_n(F) of index\n m
• Using the Steinberg algebra model to determine the center of any Leavitt\n path algebra
• Kumjian-Pask algebras of finitely-aligned higher-rank graphs
• A Groupoid Approach to Discrete Inverse Semigroup Algebras

Related

• On the length of a class of maximal commutative subalgebras
• Maximal commutative subalgebras of a Grassmann algebra
• Algebras of quotients of path algebras
• Commutative subalgebras of the Grassmann algebra
• Commutative subalgebras of U(\mathfrak q) of maximal transcendence degree