Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science

2017-09-22

2017

Pantavos Petros

Αριστείδης Κοντογεώργης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Ιωάννης Σακελλαρίδης, Επίκουρος Καθηγητής, Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών, ΕΜΠ

Η ομολογία André-Quillen για μεταθετικές άλγεβρες

Greek

André-Quillen homology of commutative algebras

André-Quillen homology is a homology theory of commutative algebras, which can be thought of as the "derived functor" of Kähler differentials. It is a special case of Quillen homology, which can be thought of as the "derived functor" of abelianization. We begin this thesis by sketching the notion of derived functors, which comes from homological algebra. However, homological algebra deals only with abelian categories (a generalization of categories of R-modules), while the categories of commutative R-algebras that we are interested in, are far from being abelian. Thus, in order to define André-Quillen homology, we will have to generalize the notion of derived functors. We will need two tools. Namely, simplicial objects and model categories. We describe these tools after presenting Kähler differentials. Then, we talk about the abelianization functor and Quillen homology. Finally, we show that Kähler differentials are a special case of the abelianization functor, and we conclude with the notion of André-Quillen homology.

Science

Quillen homology, André-Quillen homology, Kähler differentials, homotopical algebra

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https://pergamos.lib.uoa.gr/uoa/dl/object/1933148