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Seminar for Mathematical Logic

PROGRAM

Plan rada Seminara za logiku za decembar 2015.

Seminar za matematicku logiku Matematickog instituta SANU nastavlja rad u letnjem semestru 2011/2012.g. na ovoj adresi: Kneza Mihaila 36/III sprat, soba 301f - sala za seminare. Cetvrtkom posle podne, ali od 15:00 sati, odrzavace se predavanja na Seminaru iz verovatnosnih logika pod rukovodstvom Profesora Miodraga Raskovica koji je u decembru 2007. dobio akreditaciju Naucnog veca Instituta. Na taj nacin, ponovo, kao pre vise decenija, postoje dva logicka seminara.

PETAK, 18.12.2015. U 16:15 (MI SANU, 301f)
Esperanza Lopez Centella, Univerzitet u Granadi, Spanija
WEAK MULTIPLIER BIALGEBRAS: COMPLETING THE PICTURE

Abstract: The most well-known examples of Hopf algebras are the linear spans of (arbitrary) groups for a field k. Dually, also the vector space of k-valued functions on a finite group carries the structure of a Hopf algebra. In the case of infinite groups, however, the vector space of k-valued functions -- with finite support-- possesses no unit. Consequently, it is no longer a Hopf algebra but, more generally, a multiplier Hopf algebra [3]. Replacing groups with finite groupoids, both their linear spans and the vector spaces of k-valued functions carry weak Hopf algebra structures [2]. Finally, removing the finiteness constraint in this situation, both the linear spans of arbitrary groupoids, and the vector spaces of functions with finite support on them are examples of weak multiplier Hopf algebras as introduced in the recent paper [4]. Similar relations can be discussed between bialgebras and monoids, and weak bialgebras and categories |as long as their object sets are finite. With the ultimate aim to describe the analogous structures associated to categories with non-finite object sets, in this talk we introduce and study weak multiplier bialgebras. This notion fills the conceptual gap of the `antipodeless' situation of weak multiplier Hopf algebras by Van Daele and Wang's [4] and it is supported by the fact that the main features of weak bialgebras extend to this generalization. Most of the content of the talk will be based on [1].

[1] Gabriella Bohm, Jose Gomez Torrecillas and Esperanza Lopez Centella, Weak mul- tiplier bialgebras, Trans. Am. Math. Soc., ISSN 1088-6850 (online), ISSN 0002-9947 (print), [arXiv:1306.1466].

[2] G. Bohm, F. Nill and K. Szlachanyi, Weak Hopf algebras. I. Integral theory and C*- structure, J. Algebra 221 (1999), no. 2, 385{438, [arXiv:9805116].

[3] A. Van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), no. 2, 917-932, [arXiv:9803005].

[4] A. Van Daele and S. Wang, Weak Multiplier Hopf Algebras. Preliminaries, motiva- tion and basic examples, in: Operator Algebras and Quantum Groups. W. Pusz and P.M. So ltan (eds.), Banach Center Publications (Warsaw), vol. 98 (2012), 367-415, [arXiv:1210.3954.

OBAVESTENJA:

Ukoliko zelite mesecne programe ovog Seminara u elektronskom obliku, obratite se: zpetric@mi.sanu.ac.rs ili tane@mi.sanu.ac.rs. Programi svih seminara Matematickog instituta SANU nalaze se na sajtu: www.mi.sanu.ac.rs