Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology / Reiner Hermann
Type de document : MonographieCollection : Memoirs of the American Mathematical Society, 1151Langue : anglais.Pays: Etats Unis.Éditeur : Providence (R.I.) : American Mathematical Society, 2016Description : 1 vol. (V-146 p.) : ill. ; 26 cmISBN: 9781470419950.ISSN: 0065-9266.Bibliographie : Bibliogr. p. [141]-146. Index.Sujet MSC : 16E40, Homological methods in associative algebras, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)16T05, Associative rings and algebras - Hopf algebras, quantum groups and related topics, Hopf algebras and their applications
18M05, Monoidal categories and operads, Monoidal categories, symmetric monoidal categories
18E10, Category theory; homological algebra - Categorical algebra, Abelian categories, Grothendieck categories
18G15, Homological algebra in category theory, derived categories and functors, Ext and Tor, generalizations, Künneth formulaEn-ligne : zbMath | MSN | AMS-résumé
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries AMS (Browse shelf(Opens below)) | Available | 12521-01 |
Bibliogr. p. [141]-146. Index
In this monograph, we extend S. Schwede’s exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid.
As a main result, we show that our construction behaves well with respect to structure preserving functors between exact monoidal categories. We use our main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, we further determine a significant part of the Lie bracket’s kernel, and thereby prove a conjecture by L. Menichi. Along the way, we introduce n-extension closed and entirely extension closed subcategories of abelian categories, and study some of their properties
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