LDR 02881     2200349   4500
010    _a9781470419950
011    _a0065-9266
090    _a16942
101    _aeng
102    _aUS
100    _a20150209              frey50       
200    _aMonoidal categories and the Gerstenhaber bracket in Hochschild cohomology
       _fReiner Hermann
210    _aProvidence (R.I.)
       _cAmerican Mathematical Society
215    _a1 vol. (V-146 p.)
225    _9170211
       _aMemoirs of the American Mathematical Society
320    _aBibliogr. p. [141]-146. Index
330    _aIn 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
410    _9170209
       _tMemoirs of the American Mathematical Society
676    _a2010
686    _20
       _bAssociative rings and algebras -- Homological methods
       _x(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
686    _20
       _bAssociative rings and algebras -- Hopf algebras, quantum groups and related topics
       _xHopf algebras and their applications
686    _20
       _bCategory theory; homological algebra -- Categories with structure
       _xMonoidal categories, symmetric monoidal categories, braided categories
686    _20
       _bCategory theory; homological algebra -- Abelian categories
       _xExact categories, abelian categories
686    _20
       _bCategory theory; homological algebra -- Homological algebra
       _xExt and Tor, generalizations, Künneth formula
700    _4070
856    _uhttps://zbmath.org/?q=an%3A06786968
856    _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=3518219
856    _uhttp://www.ams.org/books/memo/1151/
905    _aaw
906    _aaw
001     16942
995    _f12521-01
       _xachat Ebsco
       _kSéries AMS
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