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

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	American English
Journal	Communications in Algebra
Volume	45
DOIs	https://doi.org/10.1080/00927872.2016.1270292
State	Published - Dec 16 2016

Keywords

Differential graded algebras
Differential graded modules
Yoneda Ext

DC Disciplines

Education
Mathematics

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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.",

keywords = "Differential graded algebras, Differential graded modules, Yoneda Ext",

author = "Saeed Nasseh and Sean Sather-Wagstaff",

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year = "2016",

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language = "American English",

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T1 - Extension Groups for DG Modules

AU - Nasseh, Saeed

AU - Sather-Wagstaff, Sean

PY - 2016/12/16

Y1 - 2016/12/16

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 - Differential graded modules

KW - Yoneda Ext

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/391

U2 - 10.1080/00927872.2016.1270292

DO - 10.1080/00927872.2016.1270292

M3 - Article

SN - 0092-7872

VL - 45

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Extension Groups for DG Modules

Abstract

Keywords

DC Disciplines

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