IMAS 23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
artículos
Título:
Non-existence of graded unital homomorphisms between Leavitt algebras and their Cuntz splices
Autor/es:
ARNONE, GUIDO; CORTIÑAS, GUILLERMO
Revista:
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
Editorial:
WORLD SCIENTIFIC PUBL CO PTE LTD
Referencias:
Año: 2022
ISSN:
0219-4988
Resumen:
Let n ≥ 2, let n be the graph consisting of one vertex and n loops and let n- be its Cuntz splice. Let Ln = L(n) and Ln- = L(n-) be the Leavitt path algebras over a unital ring ℓ. Let Cm be the cyclic group on 2 ≤ m ≤∞ elements. Equip Ln and Ln- with their natural Cm-gradings. We show that under mild conditions on ℓ, which are satisfied, for example, when ℓ is a field or a principal ideal domain, there are no unital Cm-graded ring homomorphisms Ln → Ln- nor in the opposite direction.
