Invariant theory
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. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn.
1837 in science1843 in science1912 in scienceAbsolute invariantAffine curvatureAlexander AbianAlfred ClebschAlfred YoungAlgebraic differential equationAlgebraic invariantAlgebraic topologyArthur CayleyCanonizantCarl Friedrich GeiserCatalecticantCharles HermiteChevalley theoremChevalley–Iwahori–Nagata theoremChevalley–Shephard–Todd theoremChristine BachocClebsch–Gordan coefficientsClebsch–Gordan coefficients for SU(3)Combinatorics: The Rota WayCommutative algebraComplex reflection groupComplexification (Lie group)Corrado de ConciniCovariant (invariant theory)CumulantDavid HilbertDe Donder–Weyl theoryDelta setDickson's lemmaDifferential invariantDu Val singularityEduard StudyElementary symmetric polynomialElimination theoryEmmy Noether
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Invariant theory
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. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn.
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A Teoria dos Invariantes é est ...... volvimento da física moderna".
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En mathématiques, la théorie d ...... descendants les plus féconds.
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In de abstracte algebra, een d ...... tels in de invariantentheorie.
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Invariant theory is a branch o ...... minant of X, when A is in SLn.
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Teorie invariantů je podobor a ...... vé kořeny v teorii invariantů.
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Теория инвариантов — раздел об ...... ет корни в теории инвариантов.
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Теорія інваріантів — розділ аб ...... коріння в теорії інваріантів.
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不變量理論是數學的一個分支,它研究群在代數簇上的作用。不變量 ...... 然而 可能有頗複雜的幾何性質,也未必滿足應滿足的範疇論性質。
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V.L.
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i/i052350
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Popov
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Like the Arabian phoenix risin ...... the forefront of mathematics.
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The theory of invariants came ...... rth from Cayley's Jovian head.
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Invariants, theory of
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A Teoria dos Invariantes é est ...... cação de George Boole em 1841.
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En mathématiques, la théorie d ...... s symétriques, l'algèbre commu
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In de abstracte algebra, een d ...... an een gegeven lineaire groep.
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Invariant theory is a branch o ...... minant of X, when A is in SLn.
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Teorie invariantů je podobor a ...... rmacích z dané lineární grupy.
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Теория инвариантов — раздел об ...... нов перестановками переменных.
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Теорія інваріантів — розділ аб ...... членів перестановками змінних.
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不變量理論是數學的一個分支,它研究群在代數簇上的作用。不變量 ...... 然而 可能有頗複雜的幾何性質,也未必滿足應滿足的範疇論性質。
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Invariant theory
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Invarianta teorio
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Invariantentheorie
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Teoria dos invariantes
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Teorie invariantů
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Théorie des invariants
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Теория инвариантов
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Теорія інваріантів
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不變量理論
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