Homological properties of cochain Differential Graded algebras

Anders J. Frankild; Peter Jørgensen

doi:10.1016/j.jalgebra.2008.08.001

Homological properties of cochain Differential Graded algebras

Anders J. Frankild
, Peter Jørgensen^*

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

9 Citations (Scopus)

Abstract

Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap Theorem. These were inspired by homological ring theory. By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space. Indeed, this paper establishes such analogous results.

Original language	English
Journal	Journal of Algebra
Volume	320
Issue	8
Pages (from-to)	3311-3326
Number of pages	16
ISSN	0021-8693
DOIs	https://doi.org/10.1016/j.jalgebra.2008.08.001
Publication status	Published - 15 Oct 2008
Externally published	Yes

Keywords

Amplitude inequality
Auslander-Buchsbaum equality
Differential Graded modules
Gap Theorem
Homological dimensions
Homological identities
Singular cochain complexes
Topological spaces

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title = "Homological properties of cochain Differential Graded algebras",

abstract = "Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap Theorem. These were inspired by homological ring theory. By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space. Indeed, this paper establishes such analogous results.",

keywords = "Amplitude inequality, Auslander-Buchsbaum equality, Differential Graded modules, Gap Theorem, Homological dimensions, Homological identities, Singular cochain complexes, Topological spaces",

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year = "2008",

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doi = "10.1016/j.jalgebra.2008.08.001",

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T1 - Homological properties of cochain Differential Graded algebras

AU - Frankild, Anders J.

AU - Jørgensen, Peter

PY - 2008/10/15

Y1 - 2008/10/15

N2 - Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap Theorem. These were inspired by homological ring theory. By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space. Indeed, this paper establishes such analogous results.

AB - Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality, an Auslander-Buchsbaum Equality, and a Gap Theorem. These were inspired by homological ring theory. By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space. Indeed, this paper establishes such analogous results.

KW - Amplitude inequality

KW - Auslander-Buchsbaum equality

KW - Differential Graded modules

KW - Gap Theorem

KW - Homological dimensions

KW - Homological identities

KW - Singular cochain complexes

KW - Topological spaces

UR - https://www.scopus.com/pages/publications/51249122835

U2 - 10.1016/j.jalgebra.2008.08.001

DO - 10.1016/j.jalgebra.2008.08.001

M3 - Journal article

AN - SCOPUS:51249122835

SN - 0021-8693

VL - 320

SP - 3311

EP - 3326

JO - Journal of Algebra

JF - Journal of Algebra

IS - 8

ER -

Homological properties of cochain Differential Graded algebras

Abstract

Keywords

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