Speaker
Description
In 1971., Steven J. Takiff, while studying invariant polynomial rings, defined a specific extension of the finite-dimensional Lie algebra. In his honor, mathematicians call the corresponding extensions of finite-dimensional simple Lie algebras, but also of some infinite-dimensional Lie algebras, Takiff algebras. Takiff algebras are also known as truncated current Lie algebras or polynomial Lie algebras. They are strongly related to the Galilean algebras known in (mathematical) physics.
In this talk, we will define the Takiff algebra obtained from the affine Lie algebra of type $A_1^{(1)}$ and explain construction of its associated vertex algebra and the vertex operator algebra. In addition, we will present some important properties of the previous structures.
