The Lie algebra

This article aims to introduce this important mathematical theory to the community of Vietnamese mathematicians in a hope to bring more attention of Vietnamese mathematicians and math students to this vibrant research area.

8p viling 11-10-2024 0 0   Download

For example, we still don’t know if it has the structure of an algebraic group of infinite dimension. In this paper, we will construct the Cremona group functor, calculate its Lie algebra and show that its Lie algebra is simple.

11p tamynhan9 02-12-2020 6 1   Download

We prove that the existence of the normal polarization associated with a linear functional on the Lie algebra is necessary and sufficient for the linear transition to local canonical Darboux coordinates (p, q) on the coadjoint orbit.

8p cumeo2008 02-07-2018 32 1   Download

We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber.

48p dontetvui 17-01-2013 35 6   Download

We define and study an algebra Ψ∞ (M0 ) of pseudodifferential opera1,0,V tors canonically associated to a noncompact, Riemannian manifold M0 whose geometry at infinity is described by a Lie algebra of vector fields V on a compactification M of M0 to a compact manifold with corners. We show that the basic properties of the usual algebra of pseudodifferential operators on a compact manifold extend to Ψ∞ (M0 ).

32p noel_noel 17-01-2013 40 6   Download

Annals of Mathematics By Curtis T. McMullen* .Annals of Mathematics, 165 (2007), 397–456 Dynamics of SL2(R) over moduli space in genus two By Curtis T. McMullen* Abstract This paper classifies orbit closures and invariant measures for the natural action of SL2 (R) on ΩM2 , the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two. Contents 1. Introduction 2. Dynamics and Lie groups 3. Riemann surfaces and holomorphic 1-forms 4. Abelian varieties with real multiplication 5. Recognizing eigenforms 6. Algebraic sums of 1-forms 7. Connected sums of 1-forms 8.

61p noel_noel 17-01-2013 53 6   Download

Dedicated to Yum-Tong Siu for his 60th birthday. Abstract Let {X1 , . . . , Xp } be complex-valued vector fields in Rn and assume that they satisfy the bracket condition (i.e. that their Lie algebra spans all vector fields). Our object is to study the operator E = Xi∗ Xi , where Xi∗ is the L2 adjoint of Xi . A result of H¨rmander is that when the Xi are real then E is o hypoelliptic and furthemore it is subelliptic (the restriction of a destribution u to an open set U is “smoother” then the restriction...

45p noel_noel 17-01-2013 46 7   Download

We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold. 1. Introduction The space of smooth first order linear differential operators on Rn that preserve harmonic functions is closed under Lie bracket. For n ≥ 3, it is finitedimensional (of dimension (n2 + 3n + 4)/2). Its commutator subalgebra is isomorphic to so(n + 1, 1), the Lie algebra of conformal motions of Rn .

22p noel_noel 17-01-2013 46 6   Download

We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem. This method was recently introduced in [CZ] for the case of curves, leading to a new proof of Siegel’s celebrated theorem that any affine algebraic curve defined over a number field has only finitely many S-integral points, unless it has genus zero and not more than two points at infinity. Here, under certain conditions involving the intersection matrix of the divisors at infinity, we shall conclude that the integral points on a surface all lie on a curve. We shall...

23p tuanloccuoi 04-01-2013 53 6   Download

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers. 1. Introduction 1.1. Let g be a simple Lie algebra over C. The main aim of this paper is to prove the following unique factorisation of tensor products of irreducible, finite dimensional representations of g:

23p tuanloccuoi 04-01-2013 50 6   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset...

42p thulanh3 10-09-2011 53 5   Download

In §2.4 the case of a tridiagonal matrix was treated specially, because that particular type of linear system admits a solution in only of order N operations, rather than of order N 3 for the general linear problem. When such particular types exist

7p babyuni 17-08-2010 76 3   Download

A system of linear equations is called sparse if only a relatively small number of its matrix elements aij are nonzero. It is wasteful to use general methods of linear algebra on such problems, because most of the O(N 3 ) arithmetic operations devoted to solving the set of equations or inverting the matrix involve zero operands. Furthermore, you might wish to work problems so large as to tax your available memory space, and it is wasteful to reserve storage for unfruitful zero elements.

20p babyuni 17-08-2010 83 8   Download

Iterative improvement of the solution to A · x = b. The first guess x + δx is multiplied by A to produce b + δb. The known vector b is subtracted, giving δb. The linear set with this right-hand side is inverted, giving δx.

5p babyuni 17-08-2010 58 2   Download

A quick-and-dirty way to solve complex systems is to take the real and imaginary parts of (2.3.16), giving A·x−C·y=b (2.3.17) C·x+A·y=d which can be written as a 2N × 2N set of real equations

6p babyuni 17-08-2010 62 3   Download

Notice the essential difference between equation (2.1.8) and equation (2.1.6). In the latter case, the C’s must be applied to b in the reverse order from that in which they become known. That is, they must all be stored along the way.

3p babyuni 17-08-2010 58 6   Download

x[i]=sum/p[i]; } } A typical use of choldc and cholsl is in the inversion of covariance matrices describing the fit of data to a model; see, e.g., §15.6. In this, and many other applications, one often needs L−1 . The lower triangle of this matrix can be efficiently found from the output of choldc: for (i=1;i

5p babyuni 17-08-2010 74 2   Download