Invariant theory
노트
위키데이터
- ID : Q1855669
말뭉치
- Turnbull’s work on invariant theory built on the symbolic methods of the German mathematicians Rudolf Clebsch (1833-1872) and Paul Gordan (1837-1912).[1]
- This paper presents a simple graphical method, closely related to the “algebrochemical method” of Clifford and Sylvester, for computations in the classical invariant theory of binary forms.[2]
- One of the first objects of study in invariant theory were the so-called invariants of forms.[3]
- Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions.[4]
- Modern research in invariant theory of finite groups emphasizes "effective" results, such as explicit bounds on the degrees of the generators.[4]
- Invariant theory of infinite groups is inextricably linked with the development of linear algebra, especially, the theories of quadratic forms and determinants.[4]
- Another subject with strong mutual influence was projective geometry, where invariant theory was expected to play a major role in organizing the material.[4]
- A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra.[5]
- Classically, invariant theory studies orbits under group actions, orbit closures, and the equations that vanish on them.[6]
- These invariant theory structures were studied classically by mathematicians including David Hilbert and Emmy Noether.[6]
- This picture describes our invariant theory set-up.[6]
- Invariant theory is a classical subject whose history is deeply intertwined with the foundations of algebraic geometry.[7]
- The core topic will be geometric invariant theory, but aspects of computational invariant theory, and what might be termed arithmetic invariant theory will also be explored.[7]
- Geometric invariant theory is an essential tool for constructing moduli spaces in algebraic geometry, but there are many moduli problems which do not neatly fit into this framework.[8]
- Recently a theory has emerged which treats the results and structures of geometric invariant theory in a broader context.[8]
- The general equivalence is demonstrated, so far as elementary applications are concerned, of the method of tensors with the classical symbolic method of invariant theory.[9]
- Part III consists of applications to the classical problems of invariant theory.[9]
- Geometric Invariant Theory was developed by Mumford to construct quotients in algebraic geometry.[10]
- So my question is pretty much summed up by the summary - basically I've run into a need to teach myself some of the basics of invariant theory and was looking for a good place to start.[11]
- The book starts with an introduction to Geometric Invariant Theory (GIT).[12]
- That this is actually the case is one of the main results of Hilbert’s landmark paper of 1890, a paper which would be the cause of the “first demise” of invariant theory.[13]
소스
- ↑ Invariant theory | mathematics
- ↑ Graph theory and classical invariant theory
- ↑ Invariants, theory of
- ↑ 4.0 4.1 4.2 4.3 Invariant theory
- ↑ AMS :: Transactions of the American Mathematical Society
- ↑ 6.0 6.1 6.2 Invariant theory for Maximum Likelihood Estimation
- ↑ 7.0 7.1 ETH :: D-MATH :: Invariant Theory
- ↑ 8.0 8.1 Beyond geometric invariant theory
- ↑ 9.0 9.1 Invariant theory, tensors and group characters
- ↑ Instability in Invariant Theory
- ↑ Resources on Invariant Theory
- ↑ European Mathematical Society Publishing House
- ↑ The Invariant Theory of Matrices
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위키데이터
- ID : Q1855669