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 ...

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) ...

This is a preview. Log in through your library . Abstract Let k be a commutative ring with unit of characteristic $p > 0$ and let G = Spec(A) be an affine commutative ...

Courtney Gibbons is affiliated with the Association for Women in Mathematics and the American Mathematical Society. You might remember learning about the quadratic formula to figure out the solutions ...

Let $G$ be a connected, simply connected nilpotent Lie group, $H$ a Lie subgroup, and $\sigma$ an irreducible unitary representations of $H$. In a previous paper, the ...

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 ...

A research team of mathematicians and computer scientists has used machine learning to reveal new mathematical structure within the theory of finite groups. By training neural networks to recognise ...

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 ...