In arithmetic geometry, the Weil–Châtelet group or WC-group of an algebraic group such as an abelian variety A defined over a field K is the abelian group of principal homogeneous spaces for A, defined over K. John Tate named it for François Châtelet who introduced it for elliptic curves, and André Weil, who introduced it for more general groups. It plays a basic role in the arithmetic of abelian varieties, in particular for elliptic curves, because of its connection with infinite descent.
In mathematics, Harish-Chandra's regularity theorem, introduced by Harish-Chandra, states that every invariant eigendistribution on a semisimple Lie group, and in particular every character of an irreducible unitary representation on a Hilbert space, is given by a locally integrable function. Harish-Chandra proved a similar theorem for semisimple p-adic groups.
John Hilton Grace FRS was a British mathematician. The Grace–Walsh–Szegő theorem is named in part after him.
In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. The concept is named after Kunihiko Kodaira.
In algebraic geometry, the Mumford vanishing theorem proved by Mumford in 1967 states that if L is a semi-ample invertible sheaf with Iitaka dimension at least 2 on a complex projective manifold, then
In mathematics, an Arf ring was defined by Lipman (1971) to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied by Cahit Arf.
In the mathematical theory of automorphic representations, a multiplicity-one theorem is a result about the representation theory of an adelic reductive algebraic group. The multiplicity in question is the number of times a given abstract group representation is realised in a certain space, of square-integrable functions, given in a concrete way.
The Classical Groups: Their Invariants and Representations is a mathematics book by Hermann Weyl, which describes classical invariant theory in terms of representation theory. It is largely responsible for the revival of interest in invariant theory, which had been almost killed off by David Hilbert's solution of its main problems in the 1890s.
Mildred Leonora Sanderson was an American mathematician, best known for her mathematical theorem concerning modular invariants.
In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic. The study of modular invariants was originated in about 1914 by Dickson (2004).
In mathematical invariant theory, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables x and y that remains invariant under the special linear group acting on the variables x and y.
In mathematical invariant theory, the catalecticant of a form of even degree is a polynomial in its coefficients that vanishes when the form is a sum of an unusually small number of powers of linear forms. It was introduced by Sylvester (1852); see Miller (2010). The word catalectic refers to an incomplete line of verse, lacking a syllable at the end or ending with an incomplete foot.
In algebra, the Amitsur–Levitzki theorem states that the algebra of n × n matrices over a commutative ring satisfies a certain identity of degree 2n. It was proved by Amitsur and Levitsky. In particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2n.
In the mathematical theory of Kleinian groups, the Ahlfors finiteness theorem describes the quotient of the domain of discontinuity by a finitely generated Kleinian group. The theorem was proved by Lars Ahlfors, apart from a gap that was filled by Greenberg (1967).
Otto Franz Georg Schilling was a German-American mathematician known as one of the leading algebraists of his time.
This page is a glossary of terms in invariant theory. For descriptions of particular invariant rings, see invariants of a binary form, symmetric polynomials. For geometric terms used in invariant theory see the glossary of classical algebraic geometry. Definitions of many terms used in invariant theory can be found in, ,, ,, ,, , and the index to the fourth volume of Sylvester's collected works includes many of the terms invented by him.
Oliver Edmunds Glenn was an American mathematician at the University of Pennsylvania who worked on finite groups and invariant theory.
In mathematics, a ternary cubic form is a homogeneous degree 3 polynomial in three variables.
In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables.
Charles Chapman Pugh is an American mathematician who researches dynamical systems. Pugh received his PhD under Philip Hartman of Johns Hopkins University in 1965, with the dissertation The Closing Lemma for Dimensions Two and Three. He has since been a professor, now emeritus, at the University of California, Berkeley.
