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Showing 1 to 20 of 79 for “"Lie algebra"”.
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Analytic Group Kernels and Lie Algebra Kernels
Made available in DSpace on 2014-12-05T21:50:04Z (GMT). No. of bitstreams: 1 0013519.pdf: 4191483 bytes, checksum: 8be73568683b59703b526632ade49bfc (MD5) Previous issue date: 1955
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Octonions and the Exceptional Lie Algebra g_2
… 1939 entitled "Cayley Numbers and Normal Simple Lie Algebras of Type G". We prove that the algebra of derivations on the octonions is a Lie algebra of type G_2. The proof proceeds by showing the set of derivations on the octonions is a Lie algebra, has dimension fourteen, and is semisimple. Next, …
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The Lie algebra of the N=2-string
In dieser Arbeit wird die Lie Algebra des N=2-Strings, der sich auf einem Torus bewegt, konstruiert, einige Eigentschaften untersucht und insbesondere gezeigt, daß diese keine Verallgemeinerte Kac-Moody Algebra darstellt.
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Lie algebra cohomology and the representations of semisimple Lie groups
Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics.
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
We give a method for using explicitly known Lie symmetries of a system of differential equations to help find more symmetries of the system. A Lie (or infinitesimal) symmetry of a system of differential equations is a transformation of its dependent and independent variables, depending on …
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A study of vertex operator constructions for some infinite dimensional lie algebras
… thesis we construct a module for the toroidal Lie algebra and the extended toroidal Lie algebra of type A₁. The Fock module representation obtained here is faithful and completely reducible over the extended toroidal Lie algebra. We also study the level two vertex operator representation of the …
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Modules over affine lie algebras at critical level and quantum groups by Qian Lin.
There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of …
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Nonstandard Methods in Lie Theory
"In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which …
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Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras
… multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.
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High accuracy computational methods for the semiclassical Schrödinger equation
… regime. Our analysis takes place in the Lie algebra generated by multiplicative operators and polynomials of the differential operator. This Lie algebra is completely characterised by Jordan polynomials in the differential operator, which constitute naturally symmetrised differential …
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Vertex algebras generated by primary fields of low conformal weight
We classify a certain class of vertex algebras, finitely generated by a Virasoro field and even (resp. odd) primary fields of conformal weight 1 (resp 3/2). This is the first interesting case to consider when looking at finitely generated vertex algebras containing a Virasoro field (the most …
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Laguerre functions associated to Euclidean Jordan algebras
… derived from the representations of a specific Lie algebra on L<sup>2</sup>(Ω,dμ<sub>v</sub>). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are …
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Controllability and Observability of a Large Scale Thermodynamical System via Connectability Approach
… which equivalents to the analytical method of Lie algebra rank condition. The graph theory of a directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and …
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Rare events and dynamics in non-equilibrium systems
… but nevertheless belong to disciplines that lie within the purview soft matter physics. In the first part, we study the infinite-dimensional probability space of stochastic differential equations. In particular, we study the transition path ensemble (TPE), the set of transition paths between …
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Dual Pairs and Disconnected Reductive Groups
… invariant theory,” he introduces the notion of a Lie algebra dual pair (a pair (g₁, g₂) of reductive Lie subalgebras of a Lie algebra g such that g₁ and g₂ equal each other’s centralizers in g) and the notion of a Lie group dual pair (a pair (G₁, G₂) of reductive subgroups of a reductive Lie group …
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The Classical Lie algebras are more simple than they may appear
… this dissertation is to consider the classical Lie Algebras, namely: so(n, C), sl(n, C) and sp(n, C), n ≥ 2. Our aim will be to prove that if a Lie Algebra L is classical, except for so(2, C) and so(4, C), then it is simple. The classification and analysis will include finding their root systems …
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Rings of regular functions on spherical nilpotent orbits for complex classical groups
Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a G-module. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits.
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On hochschild cohomology and modular representation theory
… theory of finite groups using the (restricted) Lie algebra structure of the first degree of Hochschild cohomology of a block algebra B as a main tool. This lead to two directions: In the first part we investigate the global approach. In particular, we prove the compatibility of the p-power map …
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Poisson-lie structures on infinite-dimensional jet groups and their quantization
We study the problem of classifying all Poisson-Lie structures on the group Gy of local diffeomorphisms of the real line R¹ which leave the origin fixed, as well as the extended group of diffeomorphisms G₀<sub>∞</sub> ⊃ G<sub>∞</sub> whose action on R¹ does not necessarily fix the origin. A …
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Categories with projective functors
… category with projective functors. It is then applied to describe the right (or left) exact functors on various categories of representations of semi simple Lie algebras. Other applications are the description of the algebra of adjoint finite endomorphisms of a simple module with minimal …
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