[PDF] Top 20 The Hyperbolic Kac-Moody Lie Algebra of Type G_2^(1) and its Root Multiplicities.
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The Hyperbolic Kac-Moody Lie Algebra of Type G_2^(1) and its Root Multiplicities.
... and Lie algebras arose out of the study of symmetries of algebraic and geometric objects ...simple Lie Algebras. In the 1960’s interest in infinite-dimensional Lie algebras led to several ... See full document
135
Classification of Orbifold Modules under an Automorphism of Order Two.
... = 1 and σ = −1. For a root lattice of a simply-laced Lie algebra of finite type, the lattice vertex algebra gives a representation of the associated affine ... See full document
114
A Study on the Root Systems and Dynkin diagrams associated with QHA2(1)
... considered and are realized as graded Kac-Moody algebras of quasi hyperbolic type in [17 - 21]. For the same, using the homological theory and spectral sequences techniques developed by ... See full document
8
Root multiplicities of the indefinite type Kac-Moody algebras HC[subscript n]1
... the root α of g to be the level of the weight α of g 0 . Root multiplicities of all level two roots of HA (1) 1 were computed in [6] and for all level two roots of E 10 in ...for ... See full document
132
On the Quasi Hyperbolic Kac Moody Algebra QHA7(2)
... of Kac- Moody algebra [2],[3]. Kac [2], introduced the concepts of strictly imaginary roots for Kac-Moody ...of Kac- Moody algebras possessing strictly imaginary ... See full document
6
Root Multiplicities of the Indefinite Type Kac-Moody Algebra HD_n^(1).
... a hyperbolic Kac-Moody algebra of rank n + 2, though this hase been disproven in the case HC 2 (1) ...the root multiplicities of the HD 4 (1) root −2α ... See full document
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Root Multiplicities of the Indefinite Kac-Moody Lie Algebra HD_4^{(3)}
... and Lie groups are closely related to the study of symmetries in nature and are naturally related with numerous physical ...simple Lie algebras were completely classified around 1894 by ...Victor Kac ... See full document
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The Affine Lie Algebra s^ln(C) and its Z-algebra Representation.
... of its vacuum space, which is the subspace of vectors that are annihilated by the positive part of the Heisenberg ...give Lie theoretic proofs of Rogers-Ramanujan ... See full document
53
The Kostant partition functions for twisted Kac Moody algebras
... 7. Conclusion. We obtainedthe general structure of the generating functional for the KPF for an arbitrary twistedaffine algebra. The recursive relation for the KPF may be obtainedin any specific example by a simple ... See full document
17
2D Kac-Moody symmetry of 4D Yang-Mills theory
... The nonabelian interactions of Yang-Mills theory lead to some surprising new features that are not present in parallel analyses of gravity [12, 13] and QED [15]. As pointed out to us by S. Caron-Huot [38, 39], the ... See full document
20
Algebraic Structures of Certain Lie Algebras of Polynomial Fields
... ): its source (or domain) X and goal (or codomain) Y , what note that f : domain) X and goal (or codomain) Y , noted that f : X → Y (resp is associated an arrow: its identity id X : X → X ); and each pair ... See full document
11
Kostant partition functions for affine Kac Moody algebras
... Employing the method of generating functions in conjunction with various numberwe obtain recursion relations for the Kostant partition functions for the affine KacMoody algebras The part[r] ... See full document
14
Presentations : from Kac Moody groups to profinite and back
... a lot of information (cf. [PR94]), but another possibility is to see it as a (split) Kac-Moody group of affine type. This gives additional information of combinatorial nature. Indeed, this group acts ... See full document
24
Lifting k-Involutions from the Root System to the Lie Algebra.
... In the study of k-involutions one has to combine the k-structure of the group with the structure of the involution. For this one has to combine the actions on the related root data. This can be seen as follows. ... See full document
147
Affine Kac Moody groups : bounded presentations and subgroup growth
... of Lie groups and Lie algebras at the end of the 19th ...others, Lie, Killing and Cartan, and followed in the 20th century by the work of ...Dynkin. Lie theory and the study of finite simple ... See full document
123
On the Poincaré Group at the Fifth Root of Unity
... the Lie groups we use to describe particle physics, nature needs only the lower dimensional rep- resentations − an important phenomenology that we argue indicates nature is code ...(2) Lie algebra at ... See full document
17
An Introduction to Lie Algebra
... a Lie algebra simply by setting [x, y] = 0 for all vectors x and y in ...resulting Lie algebra is called ...associative algebra is abelian and therefore commutative, then ab = ba ⇔ [a, ... See full document
61
Lifting Automorphisms from Root Systems to Lie Algebras
... Some of our algorithms (and justification of the underlying theory) will depend on clever manipulation of the Chevalley constants. In particular, there may be more than one Chevalley basis for a given Lie ... See full document
474
Lie Symmetries, 1 Dimensional Optimal System and Optimal Reductions of (1 + 2) Dimensional Nonlinear Schrödinger Equation
... by Lie symmetry method. Its some approximate solutions are obtained in [3] with applying the differential transform ...The 1-soliton solution of (1) has been obtained in ...+ ... See full document
18
Kac Moody groups and cosheaves on Davis building
... The final Section 8 has similar assumptions to Section 6. We initiate the study of the homological duality for smooth G-modules. Origins of homological duality go back to Hartshorne [14]. For p-adic groups the duality ... See full document
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