Results 51 to 60 of about 297,060 (285)

Calculations on Lie Algebra of the Group of Affine Symplectomorphisms

Advances in Mathematical Physics, 2017
We find the image of the affine symplectic Lie algebra gn from the Leibniz homology HL⁎(gn) to the Lie algebra homology H⁎Lie(gn). The result shows that the image is the exterior algebra ∧⁎(wn) generated by the forms wn=∑i=1n(∂/∂xi∧∂/∂yi).
Zuhier Altawallbeh
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Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Entropy, 2016
We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
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Locally Homogeneous Manifolds Defined by Lie Algebra of Infinitesimal Affine Transformations

Mathematics, 2022
This article deals with Lie algebra G of all infinitesimal affine transformations of the manifold M with an affine connection, its stationary subalgebra ℌ⊂G, the Lie group G corresponding to the algebra G, and its subgroup H⊂G corresponding to the ...
Vladimir A. Popov
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Tensor categories of affine Lie algebras beyond admissible levels [PDF]

, 2020
We show that if V is a vertex operator algebra such that all the irreducible ordinary V -modules are $$C_1$$ C 1 -cofinite and all the grading-restricted generalized Verma modules for V are of finite length, then the category of finite length generalized
T. Creutzig, Jinwei Yang
semanticscholar   +1 more source

Galilean contractions of W-algebras

Nuclear Physics B, 2017
Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras.
Jørgen Rasmussen, Christopher Raymond
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Generic simplicity of quantum Hamiltonian reductions

Comptes Rendus. Mathématique, 2021
Let a reductive group $G$ act on a smooth affine complex algebraic variety $X.$ Let $\mathfrak{g}$ be the Lie algebra of $G$ and $\mu :T^*(X)\rightarrow \mathfrak{g}^*$ be the moment map.
Tikaradze, Akaki
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Toroidal extended affine Lie algebras and vertex algebras [PDF]

arXiv, 2021
In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $\phi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for ...
arxiv  

A Construction of the Level 3 Modules for the Affine Lie Algebra ₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type Amer. Math. Soc. 348 (1996), pp. 481-501.

, 1996
We obtain a vertex operator construction of level 3 standard representations for the affine Lie algebra A (2) 2 . As a corollary, we also get new conbinatorial identities. 0.
S. Capparelli
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Four-Point Affine Lie Algebras [PDF]

Proceedings of the American Mathematical Society, 1995
We consider Lie algebras of the form g ⊗ R \mathfrak {g} \otimes R where g \mathfrak {g} is a simple complex Lie algebra and R = C [ s , s − 1
openaire   +1 more source

A new construction of the Drinfeld–Sokolov hierarchies

Partial Differential Equations in Applied Mathematics, 2022
The Drinfeld–Sokolov hierarchies are integrable hierarchies associated with every affine Lie algebra. We present a new construction of such hierarchies, which only requires the computations of a formal Laurent series.
Paolo Casati
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