The Lie algebra

Part 1 book "Quantum theory, groups and representations - An introduction" includes content: Introduction and overview; the group U(1) and its representations; two state systems and SU(2); linear algebra review, unitary and orthogonal groups; lie algebras and lie algebra representations; the rotation and spin groups in 3 and 4 dimensions; rotations and the spin 12 particle in a magnetic field; representations of SU(2) and so(3) 9 tensor products, entanglement, and addition of spin,... and other contents.

237p muasambanhan07 18-02-2024 2 1   Download

Part 1 of ebook "Quantum field theory III: Gauge theory" provide readers with content about: the euclidean manifold as a paradigm; the euclidean space E3 (hilbert space and lie algebra structure); algebras and duality (tensor algebra, grassmann algebra, clifford algebra, lie algebra); representations of symmetries in mathematics and physics; the euclidean manifold E3; the lie group U(1) as a paradigm in harmonic analysis and geometry;...

589p damtuyetha 16-02-2023 9 3   Download

(BQ) Ebook Mathematical methods of classical mechanics (Second edition): Part 2 presents the following content: Riemannian curvature; geodesics of left-invariant metrics on lie groups and the hydrodynamics of ideal fluids; symplectic structures on algebraic manifolds; contact structures; dynamical systems with symmetries; normal forms of quadratic hamiltonians; normal forms of hamiltonian systems near stationary points and closed trajectories; theory of perturbations of conditionally periodic motion, and kolmogorov's theorem;....

219p runordie6 10-08-2022 11 2   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 5 1   Download

Let G be a connected real semisimple Lie group with finite center and θ be a Cartan involution of G. Suppose that K is the maximal compact subgroup of G corresponding to the Cartan involution θ. The coset space X = G/K is then a Riemannian symmetric space. Denote by g the Lie algebra of G and g = k + p the Cartan decomposition of g into eigenspaces of θ. Let a be a maximal abelian subspace in p and Σ be the corresponding restricted root system.

9p covid19 11-05-2020 13 0   Download

The paper is a continuation of the authors’ works [18], [19]. In [18], we consider foliations formed by the maximal dimensional K-orbits (MD5-foliations) of connected MD5-groups that their Lie algebras have 4-dimensional commutative derived ideals and give a topological classification of the considered foliations. In [19], we study K-theory of the leaf space of some of these MD5-foliations, analytically describe and characterize the Connes’ C*-algebras of the considered foliations by the method of K-functors.

10p gaunguyen6789 19-10-2019 27 0   Download

We introduce the notion of a generalized metric n-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric n-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas).

17p nutifooddau 21-01-2019 17 1   Download

Let (L, N) be a pair of Lie algebras where N is an ideal of the finite dimensional nilpotent Lie algebra L. Some upper bounds on the dimension of the Schur multiplier of (L, N) are obtained without considering the existence of a complement for N . These results are applied to derive a new bound on the dimension of the Schur multiplier of a nilpotent Lie algebra.

5p danhdanh27 07-01-2019 27 1   Download

We present a novel hierarchy of AKNS integrable couplings based on a specific semidirect sum of Lie algebras associated with sl. By applying the variational identity, we derive a bi-Hamiltonian structure of the resulting coupling systems, thereby showing their Liouville integrability.

10p danhdanh27 07-01-2019 15 1   Download

In this article we introduce a new generalization of the concept of Lie ring which we call Jacobi system and we investigate some elementary properties of these systems and their Abelian representations.

17p danhdanh27 07-01-2019 19 1   Download

In thiswork, we give the notion of braiding for categorical Lie algebrasand crossed modules of lie algebras and we give an equivalence between them.

17p danhdanh27 07-01-2019 14 1   Download

This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators. The representations are considered as 4 × 4 matrices and the relative motion for three dual spheres is considered in terms of Hamilton operators for a dual quaternion.

19p danhdanh27 07-01-2019 14 1   Download

This article is dedicated to solving the equivalence problem for a pair of third-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. We will treat 2 versions of equivalence problems: First, the direct equivalence problem, and second, an equivalence problem to determine conditions on 2 differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.

10p tuongvidanh 06-01-2019 22 2   Download

We study a class of infinite dimensional Lie algebras called generalized Witt algebras (in one variable). These include the classical Witt algebra and the centerless Virasoro algebra as important examples. We show that any such generalized Witt algebra is a semisimple, indecomposable Lie algebra which does not contain any abelian Lie subalgebras of dimension greater than one.

32p tuongvidanh 06-01-2019 30 1   Download

Using the Guichardet construction, we compute the cohomology groups of a complex of free Lie algebras introduced by Alekseev and Torossian.

7p tuongvidanh 06-01-2019 27 1   Download

In this article we introduce the notion of the equivalence relation, isoclinism, on the central extensions of Lie algebras, and determine all central extensions occurring in an isoclinism class of a given central extension. We also show that under some conditions, the concepts of isoclinism and isomorphism between the central extensions of finite dimensional Lie algebras are identical.

9p tuongvidanh 06-01-2019 20 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

In this paper, discribe some geometric charateristics of the so-called MD(5,3C)-foliations and MD(5,4)- foliations, i.e., the foliations formed by the generic orbits of co-adjoint action of MD(5,3C)-groups and MD(5,4)-groups.

9p sansan2 26-05-2018 17 2   Download

In this paper, we introduce all subalgebras of gl 3, which are 4-dimensional MDalgebras, i.e. the solvable real Lie algebras of dimension 4 such that the co-adjoint orbits of its corresponding connected and simply connected Lie groups are either orbits of dimension zero or orbits of maximal dimension.

8p tieuthi3006 16-03-2018 29 1   Download

In the study of the theory of irreducible unitary representations, is necessary to analyze and demonstrate diverse results on integral orbital of functions belonging to the cohomology Hi (g, K; V  V*), and that it is wanted they belong to the L2(G)-cohomology of their reducible unitary representations called discrete series. Then is necessary consider the Frèchet space I(G), and analyze the 2-integrability to the fibers of the space G/K, in spaces or locally compact components of G/K.

194p lyly_5 22-03-2013 46 3   Download