Tetramodules over a bialgebra form a 2-fold monoidal category
Faculty of Sciences. Mathematics and Computer Science

article

2013
Dordrecht
, 2013

Mathematics

Applied categorical structures. - Dordrecht, 1993, currens

21(2013)
:3
, p. 291-309

0927-2852

000318286100004

E

English (eng)

University of Antwerp

Let B be an associative bialgebra over any field. A module over B in the sense of deformation theory is a tetramodule over B. All tetramodules form an abelian category. This category was studied by R. Taillefer (Algebr Represent Theory 7(5):471-490, 2004) and R. Taillefer (J Algebra 276(1):259-279, 2004). In particular, she proved that for any bialgebra B, the abelian category has enough injectives, and that Ext (a (TM) aEuro parts per thousand)(B,B) in this category coincides with the Gerstenhaber-Schack cohomology of B. We prove that the category of tetramodules over any bialgebra B is a 2-fold-monoidal category, with B a unit object in it. Roughly, this means that the category admits two monoidal structures, with common unit B, which are compatible in some rather non-trivial way (the concept of an n-fold monoidal category is introduced in Baltenu et al. (Adv Math 176:277-349, 2003)). Within (yet unproven) 2-fold monoidal analogue of the Deligne conjecture, our result would imply that RHom (a (TM) aEuro parts per thousand)(B,B) in the category of tetramodules is naturally a homotopy 3-algebra.

https://repository.uantwerpen.be/docman/iruaauth/99fbcb/5393520.pdf

http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318286100004&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848

http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318286100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848

http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000318286100004&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848