@article{947500d7095048ef8af160df47f219bc,

title = "On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles",

abstract = "Assume that a basic algebra A over an algebraically closed field (Formula presented.) with a basic set A 0 of primitive idempotents has the property that (Formula presented.) for all (Formula presented.) Let n be a nonzero integer, and (Formula presented.) and (Formula presented.) two automorphisms of the repetitive category (Formula presented.) of A with jump n (namely, they send (Formula presented.) to (Formula presented.) where (Formula presented.) is the i-th copy of A in (Formula presented.) for all (Formula presented.)). If (Formula presented.) and (Formula presented.) coincide on the objects and if there exists a map (Formula presented.) such that (Formula presented.) for all morphisms (Formula presented.) then the orbit categories (Formula presented.) and (Formula presented.) are isomorphic as (Formula presented.) -graded categories.",

keywords = "Algebra isomorphisms, graded categories, group actions, orbit categories, repetitive categories",

author = "H. Asashiba and M. Kimura and K. Nakashima and M. Yoshiwaki",

note = "Funding Information: This work is partially supported by Grant-in-Aid for Scientific Research (grant nos. 25610003 and 25287001) from JSPS (Japan Society for the Promotion of Science 10.13039/501100001691), and by JST (Japan Science and Technology Agency), CREST Mathematics (10.13039/50110000338215656429). Michio Yoshiwaki was partially supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849). We would like to thank Junichi Miyachi for asking us about the existence of examples that gives a negative solution to the conjecture above, Manuel Saor{\'i}n for sending us his unpublished paper [11] (the published version of which is [10]) and Steffen Koenig for informing us the proof of Lemmas 5.1 and 5.2. Finally we also would like to thank the referee for helpful suggestions about relationships between this paper and the work of [7], which relates the main result with the inner automorphisms of algebras (see Lemma 4.3). Publisher Copyright: {\textcopyright} 2020 Taylor & Francis Group, LLC.",

year = "2020",

doi = "10.1080/00927872.2020.1826958",

language = "English",

volume = "49",

pages = "1048--1070",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

number = "3",

}