A good way to understand the structure of a finite group is through its representations. The family of representations of a group on a fixed field has several properties: it is closed by finite direct sums, by tensor products, it contains the dual space and the tensor product of two representations is (naturally) isomorphic to the tensor product of the same representations in the opposite order. The same properties are satisfied by the category of modules of a Lie algebra, as both are symmetric tensor categories.
In this talk we will introduce the notion of symmetric tensor categories, provide examples of these categories starting by those coming from groups and Lie algebras and explain some differences between the case of the complex numbers and the one of a field of positive characteristic.