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Instantons and affine Lie algebras [PDF]
Nuclear Physics B - Proceedings Supplements, 1996 Various constructions of the affine Lie algebra action on the homology group of moduli spaces of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role of mass is also explained. The detailed proofs are given in separated papers \cite{Na-algebra,Na-Hilbert}.
Hiraku Nakajima
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Noncomplete affine structures on Lie algebras of maximal class [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Every affine structure on Lie algebra 𝔤 defines a representation of 𝔤 in aff(ℝn). If 𝔤 is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent.
E. Remm, Michel Goze
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A finiteness theorem for affine Lie algebras
Journal of Algebra, 1986 Let \(G(A)\) be the Kac-Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A, H be a Cartan subalgebra, \(\Phi\) be the root system with basis \(\Pi\), \(\Gamma =\sum_{\alpha \in \Phi}{\mathbb{Z}}\alpha\) be the root lattice, (.,.) be the bilinear form and \(\rho \in H^*\) be such that \(2(\rho,\alpha) = (\alpha,\alpha)\) for all
Vinay V. Deodhar, S. Kumaresan
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W3 constructions on affine Lie algebras [PDF]
Physics Letters B, 1992 9 ...
Alex Deckmyn, S. Schrans
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Generalized teleparallel de Sitter geometries [PDF]
European Physical Journal C: Particles and Fields, 2023 Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin-connection.
A. A. Coley +3 more
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Locally extended affine Lie algebras
Journal of Algebra, 2004 22 ...
Jun Morita, Yōji Yoshii
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Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey [PDF]
, 2010 This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
Erhard Neher
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Induced Modules for Affine Lie Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P ...
Vyacheslav Futorny, Iryna Kashuba
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Covering Algebras I. Extended Affine Lie Algebras
Journal of Algebra, 2002 Covering Algebras of extended affine Lie algebras(EALA's) relative to finite order automorphisms are studied. Conditions are given for when the resulting algebra is again an EALA. This paper deals with affinizations of EALA's relative to finite order automorphisms and these algebras are generalizations of the affine Kac-Moody Lie algebras.
Bruce Allison +2 more
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Basic Representations for Classical Affine Lie Algebras
Journal of Algebra, 2000 Presented here is a construction of certain bases of basic representations for classical affine Lie algebras. The starting point is a Z-grading g = g_{-1} + g_0 + g_1 of a classical Lie algebra g and the corresponding decomposition tilde g = tilde g_{-1} + tilde g_0 + tilde g_1 of the affine Lie algebra tilde g. By using a generalization of Frenkel-Kac
Mirko Primc
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