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DTSTART;TZID=Europe/Istanbul:20260506T160000
DTEND;TZID=Europe/Istanbul:20260506T170000
DTSTAMP:20260504T035714Z
ORGANIZER;CN=Galatasaray Universitesi Matematik Seminerleri:mailto:mathsemi
 nar@galatasaray.education
UID:4mjr9mqvuls8kn5h33haccq3ds@google.com
ATTENDEE;CUTYPE=INDIVIDUAL;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=
 TRUE;CN=turkmath@listweb.bilkent.edu.tr;X-NUM-GUESTS=0:mailto:turkmath@list
 web.bilkent.edu.tr
X-GOOGLE-CONFERENCE:https://meet.google.com/cuo-tuyk-hte
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CREATED:20260504T035658Z
DESCRIPTION:<b>Title: </b>Exceptional Drinfel’d Algebroids and Rackoids<br>
 <br><b>Abstract:</b> String and M-theories dictate new symmetry notions tha
 t are absent in point-particle theories. The generalized geometry program e
 xtends usual differential geometry in a suitable manner to explain one clas
 s of these new symmetries\, known as T-duality. In particular\, Poisson-Lie
  T-duality can be understood as arising from different decompositions of th
 e Drinfel’d double of a Lie bialgebra\, which is itself a Lie algebra. Exte
 nding this to the algebroid setting leads to Drinfel’d doubles of Lie bialg
 ebroids\, which are Courant algebroids. In order to explain another class o
 f new symmetries\, called U-duality\, one needs to further extend these not
 ions. In one of our recent works\, we extended Lie bialgebroids and their D
 rinfel’d doubles to a set-up in which the vector bundles are not dual in th
 e usual sense\, and we introduced bialgebroids and their Drinfel’d doubles 
 via a calculus framework on algebroids. In this talk\, we use this framewor
 k to introduce and construct a specific type of algebroid\, which we call e
 xceptional Drinfel’d algebroids. We prove that these are algebroid versions
  of exceptional Drinfel’d algebras\, which have recently been defined in th
 e physics literature in order to extend the Lie bialgebra/T-duality relatio
 n to the U-duality case\; hence the name. We provide a mathematically rigor
 ous framework to describe these algebras and their algebroid versions in a 
 frame-independent manner\, where we use Nambu-Poisson structures and their 
 certain generalizations. Moreover\, we introduce exceptional Drinfel’d rack
 oids\, which are global versions of exceptional Drinfel’d algebroids\, anal
 ogous to the relation between a Lie group and its Lie algebra. As examples\
 , we focus on the $SL(5)$ and $E_{6(6)}$ cases\; for the latter we also use
  another extension called proto bialgebroids\, where $H$- and $R$-fluxes ar
 e present.\n\n-::~:~::~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~
 :~:~:~:~:~:~:~:~:~::~:~::-\nJoin with Google Meet: https://meet.google.com/
 cuo-tuyk-hte\nOr dial: (US) +1 915-247-5177 PIN: 224480191#\n\nLearn more a
 bout Meet at: https://support.google.com/a/users/answer/9282720\n\nPlease d
 o not edit this section.\n-::~:~::~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~:~
 :~:~:~:~:~:~:~:~:~:~:~:~:~:~:~::~:~::-
LAST-MODIFIED:20260504T035710Z
LOCATION:Galatasaray University\, Ortaköy\, Çırağan Cd. No:36\, 34349 Beşik
 taş/İstanbul\, Türkiye Room: H307\; https://meet.google.com/cuo-tuyk-hte
SEQUENCE:1
STATUS:CONFIRMED
SUMMARY:Departmental Seminar - Keremcan Doğan\, Gebze Technical University
TRANSP:OPAQUE
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