This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems...This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.展开更多
Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie...Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250： 473-484], we show that the variety ∮（g） is reducible, and not equidimensional. Irreducible components of ∮（g） and their dimensions are precisely given. As a consequence, the variety ∮（g） is not normal.展开更多
We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan ...We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.展开更多
基金The National Grand Fundamental Research 973 Program (2004CB318000) of China
文摘This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.
文摘Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250： 473-484], we show that the variety ∮（g） is reducible, and not equidimensional. Irreducible components of ∮（g） and their dimensions are precisely given. As a consequence, the variety ∮（g） is not normal.
基金supported by FAPESP(16/16445-0,18/15712-0),RFBR(18-31-00001)the President's Program Support of Young Russian Scientists(grant MK-2262.2019.1).
文摘We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.
