RT Journal Article
T1 On isomorphism conditions for algebra functors with applications to Leavitt Path Algebras
A1 Gil-Canto, Cristóbal
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Ruiz Campos, Iván
K1 Grafos, Teoría de
K1 Álgebra
AB We introduce certain functors from the category of commu-tative rings (and related categories) to that of Z-algebras (not neces-sarily associative or commutative). One of the motivating examples isthe Leavitt path algebra functor R  → L R (E) for a given graph E. Ourgoal is to find “descending” isomorphism results of the type: if F , Gare algebra functors and K ⊂ K   a field extension, under what condi-tions an isomorphism F (K   ) ∼= G (K   ) of K   -algebras implies the exis-tence of an isomorphism F (K) ∼= G (K) of K-algebras? We find somepositive answers to that problem for the so-called “extension invari-ant functors” which include the functors associated with Leavitt pathalgebras, Steinberg algebras, path algebras, group algebras, evolutionalgebras and others. For our purposes, we employ an extension of theHilbert’s Nullstellensatz Theorem for polynomials in possibly infinitelymany variables, as one of our main tools. We also remark that for exten-sion invariant functors F , G , an isomorphism F (H) ∼= G (H), for someK-algebra H endowed with an augmentation, implies the existence of anisomorphism F (S) ∼= G (S) for any commutative and unital K-algebraS.
PB Springer
YR 2023
FD 2023-07
LK https://hdl.handle.net/10630/29865
UL https://hdl.handle.net/10630/29865
LA eng
NO Mediterr. J. Math. (2023) 20:273 https://doi.org/10.1007/s00009-023-02475-2 1660-5446/23/050001-19
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026