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arXiv · 1512.08283

Hochschild (Co)Homology of Exterior Algebras using AMT

Leon Lampret·Aleš Vavpetič
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Abstract

In 'Hochschild (co)homology of exterior algebras' (Han, Xu, 2007), the authors computed the additive and multiplicative structure of $H\!H^\ast\!(A;\!A)$, where $A$ is the $n$-th exterior algebra over a field. In this paper, we derive all their results using a different method (AMT), as well as calculate the additive structure of $H\!H_k\!(A;\!A)$ and $H\!H^k\!(A;\!A)$ over $\mathbb{Z}$. We provide concise presentations of algebras $H\!H_\ast\!(A;\!A)$ and $H\!H^\ast\!(A;\!A)$, as well as determine their generators in the Hochschild complex. Lastly, we compute an explicit free resolution (spanned by multisets) of the $A^e$-module $A$ and describe the homotopy equivalence to its bar resolution.

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BibTeXRIS

Leon Lampret, Aleš Vavpetič. 2015-12-27. Hochschild (Co)Homology of Exterior Algebras using AMT. https://doi.org/10.1080/00927872.2016.1172630

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