Hochschild homology
homology theory for associative algebras over rings
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Hochschild homology
Summary
Hochschild homology is a generalized cohomology theory[1]. It draws 46 Wikipedia views per month (generalized_cohomology_theory category, ranking #1 of 2).[2]
Key Facts
- Hochschild homology's instance of is recorded as generalized cohomology theory[3].
- Hochschild homology's Freebase ID is recorded as /m/02qfyln[4].
- Hochschild homology's Stack Exchange tag is recorded as https://mathoverflow.net/tags/hochschild-cohomology[5].
- Hochschild homology's Stack Exchange tag is recorded as https://mathoverflow.net/tags/hochschild-homology[6].
- Hochschild homology's defining formula is recorded as \begin{aligned}\operatorname{HH}n(A,M)&=\operatorname{Tor}_n^{A\otimes A^{\operatorname{op}}}(A,M)\\operatorname{HH}^n(A,M)&=\operatorname{Ext}^n{A\otimes A^{\operatorname{op}}}(A,M)\end{aligned}[7].
- Hochschild homology's studied by is recorded as ring theory[8].
- Hochschild homology's studied by is recorded as homological algebra[9].
- Hochschild homology's Mathematics Subject Classification ID is recorded as 14D15[10].
- Hochschild homology's nLab ID is recorded as Hochschild cohomology[11].
- Hochschild homology's maintained by WikiProject is recorded as WikiProject Mathematics[12].
- Hochschild homology's Microsoft Academic ID is recorded as 2776648750[13].
- Hochschild homology's in defining formula is recorded as \operatorname{HH}[14].
- Hochschild homology's in defining formula is recorded as \operatorname{Tor}[15].
- Hochschild homology's in defining formula is recorded as \operatorname{Ext}[16].
- Hochschild homology's in defining formula is recorded as A[17].
- Hochschild homology's in defining formula is recorded as M[18].
- Hochschild homology's in defining formula is recorded as A^{\operatorname{op}}[19].
- Hochschild homology's OpenAlex ID is recorded as C2776648750[20].
Why It Matters
Hochschild homology draws 46 Wikipedia views per month (generalized_cohomology_theory category, ranking #1 of 2).[2] It has Wikipedia articles in 7 language editions, a strong signal of global cultural recognition.[21] It is known by 5 alternative names across languages and contexts.[22]