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Lie algebra
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Part 2 book "A course in modern mathematical physics - Froups, hilbert space and differential geometry" includes content: Topology, measure theory andintegration, distributions, hilbert spaces, quantum mechanics, differential geometry, differentiable forms, integration on manifolds, connections and curvature, lie groups and lie algebras.
346p
muasambanhan10
06-04-2024
3
0
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Part 1 book "Factorization method in quantum mechanics" includes content: Introduction, theory, lie algebras SU(2) and SU(1,1), harmonic oscillator, infinitely deep square well potential, morse potential, poschl-teller potential, pseudoharmonic oscillator.
150p
muasambanhan08
23-02-2024
3
1
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Part 2 book "Lecture notes on Group theory in physics" includes content: Continuous translations and rotations, crystal math, consequences of crystallographic symmetry, time reversal, lie groups and lie algebras, and their representations.
195p
muasambanhan07
18-02-2024
3
0
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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
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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
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(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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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