Generalised vector fields

Abstract: Given any semisimple Kac-Moody algebra g, any dominant integral weight of g and any symmetric invariant bilinear form on g, I will generalise the Lie superalgebra W(n) of formal vector fields on n odd coordinates. The Lie superalgebra of generalised vector fields has a consistent Z-grading where a central extension of g generalises gl(n) at degree 0, and the irreducible module with the given highest weight is the subspace at degree -1, generalising the n-dimensional fundamental module of gl(n). Many well known Lie superalgebras appear as special cases (possibly after imposing a restriction on the subspace at degree 1), but also new ones that have not been studied before. Under certain conditions, they are isomorphic to tensor hierarchy algebras, which are defined from a Cartan matrix by generators and relations. The tensor hierarchy algebras have been useful in the description of extended gravity theories in physics, where ordinary diffeomorphisms are generalised and unified with additional gauge transformations. The talk is based on collaborations with Martin Cederwall: 2207.12417 and work in progress.

MathematicsPhysics

Audience: researchers in the topic

Comments: Meeting ID: 925 4420 8640 Passcode: 123089

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Representations of Lie Superalgebras and Related Topics

Series comments: ● Important Dates • Registration Opening: July 26, 2023 (Mordad 04, 1402) • Registration Deadline: August 28, 2023 (Shahrivar 06, 1402)

● Contact: Asghar Daneshvar, * Email: a[dot]daneshvar[at]ipm[dot]ir * If you have any questions or problems related to the conference or the registration form, please contact the email address above.

Plenary Speakers:

• Drazen Adamovic, University of Zagreb, Croatia

• Yuly Billig, University of Carleton, Canada

• Alberto Elduque, University of Zaragoza, Spain

• Dimitar Grantcharov, University of Texas at Arlington, United States of America

• Li Luo, East China Normal University, China

• Volodymyr Mazorchuk, Uppsala university, Sweden

• Jakob Palmkvist, Orebro University, Sweden

• Jinwei Yang, Shanghai Jiaotong University, China

• Kaiming Zhao, Wilfrid Laurier University, Canada

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