Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

  • About
    • President
    • Governance
    • Partner Institutions
    • Visit
  • People
    • Management
    • Faculty
    • Postdocs
    • Visiting Scholars
    • Staff
  • Research
    • Research Groups
    • Courses
    • Seminars
  • Join Us
    • Faculty
    • Postdocs
    • Students
  • Events
    • Conferences
    • Workshops
    • Forum
  • Life @ BIMSA
    • Accommodation
    • Transportation
    • Facilities
    • Tour
  • News
    • News
    • Announcement
    • Downloads
About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Topics in Representation Theory On the PBW Property for Universal Enveloping Algebras
On the PBW Property for Universal Enveloping Algebras
Organizers
Semen Artamonov , Pavel Nikitin , Shamil Shakirov
Speaker
Anton Khoroshkin
Time
Friday, May 30, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
The classical Poincaré–Birkhoff–Witt (PBW) theorem claims that the universal enveloping algebra of any Lie algebra admits a canonical filtration such that the associated graded algebra is isomorphic to the symmetric algebra on the underlying vector space.
  Viewing the universal enveloping algebra $U(g)$ as an associative algebra whose representations correspond bijectively to those of  $g$, one can naturally extend the notion of universal enveloping algebras to broader algebraic settings — including Poisson algebras, Lie algebras with multiple compatible brackets, and other related structures.
  In this talk, I will present a necessary and sufficient condition for the PBW property to hold for such generalized enveloping algebras, formulated in the language of (colored) operads and Gröbner basis techniques. In particular, I will show that the PBW property fails for Poisson structures and holds for Lie algebras equipped with two compatible brackets.
  All necessary definitions and background will be introduced during the talk.
Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

Copyright © Beijing Institute of Mathematical Sciences and Applications

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060