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CFT Correlators and Mapping Class Group Averages. [PDF]
Commun Math PhysRomaidis I, Runkel I.
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Global Weyl Modules and Maximal Parabolics of Twisted Affine Lie Algebras
, 2018 Matthew Lee
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Affine Lie Algebra Modules and Complete Lie Algebras
Algebra Colloquium, 2006In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.
Gao, Yongcun, Meng, Daoji
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1997
This chapter is a basic introduction to affine Lie algebras, preparing the stage for their application to conformal field theory. In Sect. 14.1.1, after having introduced the affine Lie algebras per se, we show how the fundamental concepts of roots, weights, Cartan matrices, and Weyl groups are extended to the affine case.
Philippe Di Francesco +2 more
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This chapter is a basic introduction to affine Lie algebras, preparing the stage for their application to conformal field theory. In Sect. 14.1.1, after having introduced the affine Lie algebras per se, we show how the fundamental concepts of roots, weights, Cartan matrices, and Weyl groups are extended to the affine case.
Philippe Di Francesco +2 more
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Lie Algebras of Pro-Affine Algebraic Groups
Canadian Journal of Mathematics, 2002AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is ...
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Fock Representations of Lie Algebras, Loop Algebras and Affine Lie Algebras
Communications in Theoretical Physics, 1995Explicit Fock representations of the classical Lie algebras in terms of boson creation and annihilation operators with an arbitrary highest weight are derived, and a general rule to construct Fock representations of a loop algebra from a boson realization of its corresponding Lie algebra is established.
Xu-Feng Liu, Min Qian
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Functional Analysis and Its Applications, 1991
Let \(C\) be a projective complex algebraic curve with two distinguished points \(P_{\pm}\) and let \(A\) be the ring of meromorphic functions on \(C\), holomorphic outside \(\{P_{\pm}\}\). Let \(\mathfrak g\) be a complex finite dimensional simple Lie algebra. The Lie algebra \(\mathfrak g\otimes A\) and a one-dimensional central extension \(\mathfrak
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Let \(C\) be a projective complex algebraic curve with two distinguished points \(P_{\pm}\) and let \(A\) be the ring of meromorphic functions on \(C\), holomorphic outside \(\{P_{\pm}\}\). Let \(\mathfrak g\) be a complex finite dimensional simple Lie algebra. The Lie algebra \(\mathfrak g\otimes A\) and a one-dimensional central extension \(\mathfrak
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