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
Beograd,
Srdacan pozdrav,
rukovodioci seminara Zoran Petric i Predrag Tanovic