Categorical methods in representation theory of Lie superalgebras

Project Details

Description

In the study of different objects in different sciences (such as mathematics, physics, chemistry and more), the symmetries of the object play a very important role. Such symmetries can be described as certain transformations preserving the object; these transformations can be applied one after the other, thus giving an operation of composition on the set of transformations.

The collection of such transformations, along with the operation of composition, is often called a group. Such groups can be very complicated, when the object of study itself is complicated as well, but they carry a lot of information about the structure of the original objcct.

In these cases one often prefers to take a linear approximation of the group by a linear space. Such a space is equipped with an operation as well, and is called a Lie algebra. The Lie algebras give “small” linear approximations of the transformations of the original object, and can be studied very effectively using tools from linear algebra.

In our project, we propose to study a certain variation of Lie algebras, called Lie super—algebras. The term super means that the vectors in our linear (super)spaces each have an “even” and “odd” part. These superalgebras have emerged from the concept of supersymmetry developed in physics in the second half of the 20th century.

Our project concerns presentations of Lie superalgebras as synunetries of linear superspaces; we expect that our results will shed new light on the structure of symmetries of linear superspaces, and provide new tools and techniques for finding such symmetries.

StatusActive
Effective start/end date1/01/19 → …

Funding

  • United States-Israel Binational Science Foundation (BSF)

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