[geometry-ml:02883] MS seminar at Kavli IPMU -- Yoshihisa Saito (Tokyo U) -- Feb 21, 2017

[Todor Milanov]

Dear all,

I would like to announce the following Mathematics and String theory seminar at Kavli IPMU

Speaker: Yoshihisa Saito (Tokyo University)
Date:	Tue, Feb 21, 2017, 15:30 - 17:00
Place:	Kavli IPMU, Seminar Room B

Title：On quantized elliptic algebras

Abstract： Let $\mathfrak{g}$ be a semisimple Lie algebra, and $\mathfrak{g}_{tor}$ the corresponding toridal Lie algebra. Namely,  $\mathfrak{g}_{tor}$ is the universal central extension of double loop Lie algebra $\mathfrak{g}\otimes\mathbb{C}[s^{\pm 1},t^{\pm 1}]$.Around 2000, Kyoji Saito and Yoshii gave a new presentation of $\mathfrak{g}_{tor}$ by finitely many generators and relations, attached with elliptic Dynkin diagrams.

In this talk, we introduce a q-analogue of K. Saito and Yoshii's presentation, so-called ``quantum elliptic algebras''. In addition, we show that these algebras are isomorphic to quantum toroidal algebras for several types. In other words, we give a presentation of quantum toroidal algebras by finitely many generators and relations. 

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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp