"invariant theory" meaning in English

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          "text": "1993, Bernd Sturmfels, Introduction, David Hilbert, Reinhard C. Laubenbacher (translator and editor), Bernd Sturmfels (editor), Theory of Algebraic Invariants, Cambridge University Press, page xi,\nToday, invariant theory is often understood as a branch of representation theory, algebraic geometry, commutative algebra, and algebraic combinatorics. Each of these four disciplines has roots in nineteenth-century invariant theory. […] In modern terms, the basic problem of invariant theory can be categorized as follows. Let V be a K-vector space on which a group G acts linearly. In the ring of polynomial functions K[V] consider the subring K[V]ᴳ consisting of all polynomial functions on V which are invariant under the action of the group G. The basic problem is to describe the invariant ring K[V]ᴳ. In particular, we would like to know whether K[V]ᴳ is finitely generated as a K-algebra and, if so, to give an algorithm for computing generators."
        },
        {
          "ref": "2001, Gian-Carlo Rota, “What is invariant theory, really?”, in H. Crapo, D. Senato, editors, Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota, Springer,, page 41",
          "text": "Invariant theory is the great romantic story of mathematics.[…]In our century, Lie theory and algebraic geometry, differential algebra and algebraic combinatorics are all offsprings of invariant theory.",
          "type": "quotation"
        },
        {
          "ref": "2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 225",
          "text": "For a linear algebraic group G and a regular representation (#x5C;rho,V) of G, the basic problem of invariant theory is to describe the G-invariant elements (#x7B;#x5C;bigotimes#x7D;ᵏⱽ)ᴳ of the k-fold tensor product for all k.",
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        "The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions."
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        "(algebra, representation theory) The branch of algebra concerned with actions of groups on algebraic varieties from the point of view of their effect on functions."
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          "_dis1": "98 2",
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          "sense": "branch of algebra concerned with actions of groups on algebraic varieties",
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          "word": "théorie des invariants"
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          "_dis1": "13 87",
          "word": "geometric invariant theory"
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        {
          "ref": "2012, M. Chaichian, N. F. Nelipa, Introduction to Gauge Field Theories, Springer, page 4",
          "text": "The point is that, to construct locally invariant theories, new fields have to be introduced which are referred to as the gauge fields.",
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        "Used other than figuratively or idiomatically: see invariant, theory."
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    "invariant theory"
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  "word": "invariant theory"
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          "text": "1993, Bernd Sturmfels, Introduction, David Hilbert, Reinhard C. Laubenbacher (translator and editor), Bernd Sturmfels (editor), Theory of Algebraic Invariants, Cambridge University Press, page xi,\nToday, invariant theory is often understood as a branch of representation theory, algebraic geometry, commutative algebra, and algebraic combinatorics. Each of these four disciplines has roots in nineteenth-century invariant theory. […] In modern terms, the basic problem of invariant theory can be categorized as follows. Let V be a K-vector space on which a group G acts linearly. In the ring of polynomial functions K[V] consider the subring K[V]ᴳ consisting of all polynomial functions on V which are invariant under the action of the group G. The basic problem is to describe the invariant ring K[V]ᴳ. In particular, we would like to know whether K[V]ᴳ is finitely generated as a K-algebra and, if so, to give an algorithm for computing generators."
        },
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          "ref": "2001, Gian-Carlo Rota, “What is invariant theory, really?”, in H. Crapo, D. Senato, editors, Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota, Springer,, page 41",
          "text": "Invariant theory is the great romantic story of mathematics.[…]In our century, Lie theory and algebraic geometry, differential algebra and algebraic combinatorics are all offsprings of invariant theory.",
          "type": "quotation"
        },
        {
          "ref": "2009, Roe Goodman, Nolan R. Wallach, Symmetry, Representations, and Invariants, Springer, page 225",
          "text": "For a linear algebraic group G and a regular representation (#x5C;rho,V) of G, the basic problem of invariant theory is to describe the G-invariant elements (#x7B;#x5C;bigotimes#x7D;ᵏⱽ)ᴳ of the k-fold tensor product for all k.",
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      "lang": "French",
      "sense": "branch of algebra concerned with actions of groups on algebraic varieties",
      "tags": [
        "feminine"
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      "word": "théorie des invariants"
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  "word": "invariant theory"
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