Lie algebra: An algebraic structure that captures the infinitesimal aspects of continuous groups, defined by a bilinear, antisymmetric bracket satisfying the Jacobi identity.

Iwasawa Algebra: A completed group algebra associated with a p-adic Lie group, providing a framework to study non-commutative localisation and valuation theory.

Lie theory is the study of Lie groups and Lie algebras, which are mathematical objects that highlight the structural and symmetric properties inherent in geometric objects.

In 1954, the prize was given to Indian mathematician Harish Chandra for his work - in particular for his paper on some applications of the universal enveloping algebra of a semisimple Lie.