A lifting problem for DG modules

Maiko Ono; Yuji Yoshino

doi:10.1016/j.jalgebra.2020.09.013

A lifting problem for DG modules

Maiko Ono, Yuji Yoshino

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let B=A〈X|dX=t〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if Ext_Bⁿ⁺¹(N,N)=0. Furthermore such a lifting is unique up to DG isomorphisms if Ext_Bⁿ(N,N)=0.

Original language	English
Pages (from-to)	342-360
Number of pages	19
Journal	Journal of Algebra
Volume	566
DOIs	https://doi.org/10.1016/j.jalgebra.2020.09.013
Publication status	Published - Jan 15 2021

Keywords

DG algebra
DG module
Liftings

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2020.09.013

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title = "A lifting problem for DG modules",

abstract = "Let B=A〈X|dX=t〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if ExtBn+1(N,N)=0. Furthermore such a lifting is unique up to DG isomorphisms if ExtBn(N,N)=0.",

keywords = "DG algebra, DG module, Liftings",

author = "Maiko Ono and Yuji Yoshino",

note = "Funding Information: The authors are grateful to Dr. H. Minamoto for his many helpful suggestions. In fact the use of j-operator in our proof of the main theorem were implicitly suggested to the authors by him. We would like to thank Dr. S. Nasseh for his comments on the first manuscript. The second author was supported by JSPS Grant-in-Aid for Scientific Research 19K03448 . Publisher Copyright: {\textcopyright} 2020",

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AU - Ono, Maiko

AU - Yoshino, Yuji

N1 - Funding Information: The authors are grateful to Dr. H. Minamoto for his many helpful suggestions. In fact the use of j-operator in our proof of the main theorem were implicitly suggested to the authors by him. We would like to thank Dr. S. Nasseh for his comments on the first manuscript. The second author was supported by JSPS Grant-in-Aid for Scientific Research 19K03448 . Publisher Copyright: © 2020

PY - 2021/1/15

Y1 - 2021/1/15

N2 - Let B=A〈X|dX=t〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if ExtBn+1(N,N)=0. Furthermore such a lifting is unique up to DG isomorphisms if ExtBn(N,N)=0.

AB - Let B=A〈X|dX=t〉 be an extended DG algebra by the adjunction of a variable of positive even degree n, and let N be a semi-free DG B-module that is assumed to be bounded below as a graded module. We prove in this paper that N is liftable to A if ExtBn+1(N,N)=0. Furthermore such a lifting is unique up to DG isomorphisms if ExtBn(N,N)=0.

KW - DG algebra

KW - DG module

KW - Liftings

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DO - 10.1016/j.jalgebra.2020.09.013

M3 - Article

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VL - 566

SP - 342

EP - 360

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A lifting problem for DG modules

Abstract

Keywords

ASJC Scopus subject areas

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