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 ...

American Journal of Mathematics, Vol. 120, No. 6 (Dec., 1998), pp. 1277-1287 (11 pages) A theorem of Cassidy states that any Zariski closed differential algebraic subgroup of a simple linear algebraic ...

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question. Mathematics started with numbers — clear, ...

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 ...

Algebraic geometry; commutative algebra; homological algebra; algebraic K-theory. My research has been mainly in algebraic geometry, with an abiding interest in the study of algebraic cycles, ...

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

"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." Representation theory transforms abstract algebra groups into things like simpler matrices. The field’s ...