Algebraic groups form a central pillar in modern mathematics, bridging abstract algebra, geometry, and number theory. These groups, being simultaneously algebraic varieties and groups, serve as ...

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most ...

Algebra is the discipline of pure mathematics that is concerned with the study of the abstract properties of a set, once this is endowed with one or more operations that respect certain rules (axioms) ...

First cohomology groups of finite groups with nontrivial irreducible coefficients have been useful in several geometric and arithmetic contexts, including Wiles's famous paper (1995). Internal to ...

American Journal of Mathematics, Vol. 124, No. 1 (Feb., 2002), pp. 1-48 (48 pages) We consider zeta functions defined as Euler products of $W(p,p^{-s})$ over all ...

Representation theory transforms abstract algebra groups into things like simpler matrices. The field’s founder left a list ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

Algebraic groups, defined by polynomial equations, are central to modern algebraic geometry and number theory, embodying symmetry in a wide range of mathematical structures. Their study intersects ...