Extension groups for DG modules

Saeed Nasseh; Sean Sather-Wagstaff

doi:10.1080/00927872.2016.1270292

Extension groups for DG modules

Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences

Clemson University

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

5 Scopus citations

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Abstract

Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups Extⁱ _A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtⁱ _A(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

Original language	English
Pages (from-to)	4466-4476
Number of pages	11
Journal	Communications in Algebra
Volume	45
Issue number	10
DOIs	https://doi.org/10.1080/00927872.2016.1270292
State	Published - Oct 3 2017

Scopus Subject Areas

Algebra and Number Theory

Keywords

Differential graded algebras
Yoneda Ext
differential graded modules

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10.1080/00927872.2016.1270292

Cite this

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title = "Extension groups for DG modules",

abstract = "Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups Exti A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExti A(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.",

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N2 - Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups Exti A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExti A(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

AB - Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups Exti A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExti A(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

KW - Differential graded algebras

KW - Yoneda Ext

KW - differential graded modules

UR - https://www.scopus.com/pages/publications/85015650058

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JO - Communications in Algebra

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Extension groups for DG modules

Abstract

Scopus Subject Areas

Keywords

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