---
res:
bibo_abstract:
- "Let A be an associative and unital algebra over a commutative ring K, such that
A is K-projective. The Hochschild cohomology ring HH*(A) of A is, as a graded
algebra, isomorphic to the Ext-algebra of A in the category of A-bimodules. In
1963, M. Gerstenhaber established a graded Lie bracket on HH*(A) of degree -1
which he described in terms of the so called bar resolution. While the multiplication
admits an intrinsic description (Yoneda product), this Lie bracket has resisted
such an interpretation at first. A serious attempt to find a categorical description
of the Lie bracket was given by S. Schwede in 1998. By using the monoidal structure
on the category of A-bimodules, he was able to formulate Gerstenhaber's bracket
in terms of self-extensions of A. The present thesis extends Schwede's construction
to exact and monoidal categories. Therefore we will establish an explicit description
of an isomorphism by A. Neeman and V. Retakh, linking Ext-groups with fundamental
groups of categories of extensions.\r\n\r\nOur main result shows that our construction
behaves well with respect to structure preserving functors between strong exact
monoidal categories. We use our main result to conclude, that the graded Lie bracket
on HH*(A) is an invariant under Morita equivalence. For quasitriangular Hopf algebras
over K, we further determine a significant part of the Lie bracket's kernel.@eng"
bibo_authorlist:
- autoren_ansetzung:
- Hermann, Reiner
- Hermann
- Reiner Hermann
- Hermann, R
- Hermann, R.
- R Hermann
- R. Hermann
foaf_Person:
foaf_givenName: Reiner
foaf_name: Hermann, Reiner
foaf_surname: Hermann
foaf_workInfoHomepage: http://www.librecat.org/personId=18840579
dct_date: 2013^xs_gYear
dct_language: eng
dct_publisher: Universität Bielefeld@
dct_subject:
- Hopf algebras
- Representation theory
- Hochschild cohomology
- Gerstenhaber algebras
dct_title: Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology@
...