On induced graded simple modules over graded Steinberg algebras with applications to Leavitt path algebras. (English) Zbl 07815035
For an ample groupoid \(\mathcal{G}\), its Steinberg algebra is defined by B. Steinberg [Adv. Math. 223, No. 2, 689–727 (2010; Zbl 1188.22003)] and L. O. Clark et al. [Semigroup Forum 89, No. 3, 501–517 (2014; Zbl 1323.46033)]. These algebras include the well-known Leavitt path algebras and Kumjian-Pask algebras.
The paper under review studies the induction functor and restriction functor associated to Steinberg algebras in the graded setting. The spectral graded simple modules over graded Steinberg algebras are studied. Moreover, spectral simple modules and spectral graded simple modules over the Leavitt path algebras are classified; see Theorems 4.1 and 4.2.
The paper under review studies the induction functor and restriction functor associated to Steinberg algebras in the graded setting. The spectral graded simple modules over graded Steinberg algebras are studied. Moreover, spectral simple modules and spectral graded simple modules over the Leavitt path algebras are classified; see Theorems 4.1 and 4.2.
Reviewer: Xiao-Wu Chen (Hefei)
MSC:
| 16S99 | Associative rings and algebras arising under various constructions |
| 16S88 | Leavitt path algebras |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16D60 | Simple and semisimple modules, primitive rings and ideals in associative algebras |
Keywords:
graded groupoid; Steinberg algebra; Leavitt path algebra; graded simple module; Chen simple moduleReferences:
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