(Q1622047)

English

Hochschild homology

homology theory for associative algebras over rings

Hochschild cohomology

In more languages

Statements

generalized cohomology theory

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homological algebra

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defining formula

{\begin{aligned}\operatorname {HH} _{n}(A,M)&=\operatorname {Tor} _{n}^{A\otimes A^{\operatorname {op} }}(A,M)\\\operatorname {HH} ^{n}(A,M)&=\operatorname {Ext} _{A\otimes A^{\operatorname {op} }}^{n}(A,M)\end{aligned}}

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in defining formula

\operatorname {HH}

symbol represents

Hochschild homology

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\operatorname {Tor}

symbol represents

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\operatorname {Ext}

symbol represents

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A

symbol represents

associative algebra

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M

symbol represents

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A^{\operatorname {op} }

symbol represents

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maintained by WikiProject

WikiProject Mathematics

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Stack Exchange tag

https://mathoverflow.net/tags/hochschild-cohomology

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https://mathoverflow.net/tags/hochschild-homology

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Identifiers

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Freebase Data Dumps

publication date

28 October 2013

Mathematics Subject Classification ID

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Microsoft Academic ID

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Hochschild cohomology

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

Sitelinks

Wikipedia(7 entries)

dewiki Hochschild-Homologie und Kohomologie
enwiki Hochschild homology
eswiki Homología de Hochschild
frwiki Homologie de Hochschild
hewiki קוהומולוגיית הוכשילד
kowiki 호흐실트 호몰로지
zhwiki 霍赫希尔德同调

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