Unipotency
Unipotency is a property used in linear algebra, group theory, and algebraic geometry to describe a close relationship to the identity transformation. In a linear representation, an element g of GL(V) is unipotent if g − I is a nilpotent operator. Equivalently, all eigenvalues of g are equal to 1, and in a suitable basis g is a Jordan matrix with ones on the diagonal. In GL_n over a field, these conditions are equivalent; a typical form is g = I + N with N nilpotent.
Examples include the strictly upper triangular matrices with ones on the diagonal, which form a canonical unipotent
In the context of algebraic groups, a unipotent element of a linear algebraic group G is one
In Lie theory, over fields of characteristic zero, unipotent elements are closely related to nilpotent elements
Unipotent conjugacy classes in reductive groups are classified by combinatorial data, such as partitions for GL_n,