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UID:6c76452ed9951b2d3c09c14f09576343
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20230329T104443
SUMMARY: Yang-Baxter equations for vertex operator algebras and their operator forms
LOCATION:Hill 705
DESCRIPTION:<p><strong style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (W
 est European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Hel
 vetica Neue', sans-serif; font-size: 15px; letter-spacing: normal; orphans:
  2; text-align: start; text-indent: 0px; text-transform: none; white-space:
  normal; widows: 2; word-spacing: 0px; background-color: #ffffff;">Abstract
 &nbsp;</strong>The classical Yang-Baxter equation (CYBE) is the semi-classi
 cal limit of<br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI W
 eb (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto,
  'Helvetica Neue', sans-serif; font-size: 15px; font-weight: 400; letter-sp
 acing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transf
 orm: none; white-space: normal; widows: 2; word-spacing: 0px; background-co
 lor: #ffffff;" aria-hidden="true">the quantum Yang-Baxter equation, named a
 fter the physicists C.N. Yang and<br style="color: #242424; font-family: 'S
 egoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkM
 acSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; font-w
 eight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-ind
 ent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacin
 g: 0px; background-color: #ffffff;" aria-hidden="true">R. Baxter. Its solut
 ion has inspired the remarkable works of Belavin, Drinfeld,<br style="color
 : #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe 
 UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-seri
 f; font-size: 15px; font-weight: 400; letter-spacing: normal; orphans: 2; t
 ext-align: start; text-indent: 0px; text-transform: none; white-space: norm
 al; widows: 2; word-spacing: 0px; background-color: #ffffff;" aria-hidden="
 true">and others and the important notions of Lie bialgebras and Manin trip
 les.<br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West
  European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvet
 ica Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spacing: n
 ormal; orphans: 2; text-align: start; text-indent: 0px; text-transform: non
 e; white-space: normal; widows: 2; word-spacing: 0px; background-color: #ff
 ffff;" aria-hidden="true">Motivated by the importance of the CYBE in the th
 eory and applications of<br style="color: #242424; font-family: 'Segoe UI',
  'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemF
 ont, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; font-weight: 40
 0; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px;
  text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; b
 ackground-color: #ffffff;" aria-hidden="true">Lie algebras, various analogs
  of the CYBE for other algebraic structures have<br style="color: #242424; 
 font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple
 -system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-siz
 e: 15px; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: 
 start; text-indent: 0px; text-transform: none; white-space: normal; widows:
  2; word-spacing: 0px; background-color: #ffffff;" aria-hidden="true">been 
 extensively studied in recent years. In this talk, we will first review the
 <br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West Eur
 opean)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica 
 Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spacing: norma
 l; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; w
 hite-space: normal; widows: 2; word-spacing: 0px; background-color: #ffffff
 ;" aria-hidden="true">tensor and operator forms of the CYBE and their conne
 ctions with the<br style="color: #242424; font-family: 'Segoe UI', 'Segoe U
 I Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Robo
 to, 'Helvetica Neue', sans-serif; font-size: 15px; font-weight: 400; letter
 -spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-tra
 nsform: none; white-space: normal; widows: 2; word-spacing: 0px; background
 -color: #ffffff;" aria-hidden="true">Rota-Baxter operators. Then we will gi
 ve a generalization of the CYBE in both<br style="color: #242424; font-fami
 ly: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, 
 BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; 
 font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; te
 xt-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-
 spacing: 0px; background-color: #ffffff;" aria-hidden="true">tensor and ope
 rator form to the vertex operator algebras, which provides us<br style="col
 or: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Sego
 e UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-se
 rif; font-size: 15px; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: start; text-indent: 0px; text-transform: none; white-space: no
 rmal; widows: 2; word-spacing: 0px; background-color: #ffffff;" aria-hidden
 ="true">with a parameter-independent Yang-Baxter equation whose solutions l
 ie in<br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (Wes
 t European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helve
 tica Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spacing: 
 normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: no
 ne; white-space: normal; widows: 2; word-spacing: 0px; background-color: #f
 fffff;" aria-hidden="true">an infinite-dimensional vector space. Finally, w
 e will discuss its relations with<br style="color: #242424; font-family: 'S
 egoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkM
 acSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; font-w
 eight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-ind
 ent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacin
 g: 0px; background-color: #ffffff;" aria-hidden="true">the CYBE. No prior k
 nowledge of Yang-Baxter equations is required. This talk is<br style="color
 : #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe 
 UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-seri
 f; font-size: 15px; font-weight: 400; letter-spacing: normal; orphans: 2; t
 ext-align: start; text-indent: 0px; text-transform: none; white-space: norm
 al; widows: 2; word-spacing: 0px; background-color: #ffffff;" aria-hidden="
 true">based on a joint work with Chengming Bai and Li Guo.</p>
CONTACT:Jianqi Liu, University of California at Santa Cruz
DTSTAMP:20260828T093747
DTSTART;TZID=America/New_York:20230407T121000
DTEND;TZID=America/New_York:20230407T131000
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
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